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Deck 12: B: linear Regression and Correlation
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Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
Refer to Salary and Years Narrative. Does a linear relationship exist between x and y? Test using
= 0.05.
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%Refer to Salary and Years Narrative. Does a linear relationship exist between x and y? Test using
= 0.05. Question
Question
Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
Refer to Salary and Years Narrative. What are the values of
and the sum of squares for error?
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%Refer to Salary and Years Narrative. What are the values of
and the sum of squares for error? Question
Question
Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
Refer to Salary and Years Narrative. What is the least-squares regression equation?
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%Refer to Salary and Years Narrative. What is the least-squares regression equation?
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Question
Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
Refer to Salary and Years Narrative. What are the least-squares estimates of the slope and the y-intercept?
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%Refer to Salary and Years Narrative. What are the least-squares estimates of the slope and the y-intercept?
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Question
Question
Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
Refer to Salary and Years Narrative. Find and interpret the coefficient of determination.
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%Refer to Salary and Years Narrative. Find and interpret the coefficient of determination.
Question
Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
Refer to Salary and Years Narrative. Find and interpret the correlation coefficient.
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%Refer to Salary and Years Narrative. Find and interpret the correlation coefficient.
Question
Advertising and Money Spent Narrative
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Use a statistical software package of your choice and report the regression analysis results.
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Use a statistical software package of your choice and report the regression analysis results.
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Question
Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
Refer to Salary and Years Narrative. Interpret the estimated slope and y-intercept for this .
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%Refer to Salary and Years Narrative. Interpret the estimated slope and y-intercept for this .
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Question
Advertising and Money Spent Narrative
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Develop a scatterplot and determine whether a linear relationship appears to provide a good fit to this data set.
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Develop a scatterplot and determine whether a linear relationship appears to provide a good fit to this data set.
Question
Advertising and Money Spent Narrative
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. What is the least-squares regression line?
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. What is the least-squares regression line?
Question
Wind Velocity and Windmills Narrative
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x.
s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%
Analysis of Variance
-Refer to Wind Velocity and Windmills Narrative. One of the assumptions about the random error
in the regression model is that the values of 
have a common variance equal to 
. What is the best estimator of ?
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x.
s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%Analysis of Variance
-Refer to Wind Velocity and Windmills Narrative. One of the assumptions about the random error
in the regression model is that the values of have a common variance equal to . What is the best estimator of ? Question
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Determine the coefficient of determination and discuss what its value tells you about the two variables.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Determine the coefficient of determination and discuss what its value tells you about the two variables.
Question
Advertising and Money Spent Narrative
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Calculate
and SSE for these data.
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Calculate
and SSE for these data. Question
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Estimate with 95% confidence the average monthly sales of all salespersons with ten years of experience.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Estimate with 95% confidence the average monthly sales of all salespersons with ten years of experience.
Question
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between years of experience and sales.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between years of experience and sales.
Question
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Calculate the Pearson correlation coefficient. What sign does it have? Why?
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Calculate the Pearson correlation coefficient. What sign does it have? Why?
Question
Wind Velocity and Windmills Narrative
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x. s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%
Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. Predict the DC output for a wind velocity of 22 km/h.
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x.
s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. Predict the DC output for a wind velocity of 22 km/h.
Question
Correlation between Shoreline Erosion and Rainfall
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below.
s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%
Analysis of Variance
Refer to Correlation Between Shoreline Erosion and Rainfall. Identify and interpret the coefficient of determination.
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below.
s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%Analysis of Variance
Refer to Correlation Between Shoreline Erosion and Rainfall. Identify and interpret the coefficient of determination.
Question
Wind Velocity and Windmills Narrative
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x. s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%
Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. . Identify and interpret the coefficient of determination.
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x.
s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. . Identify and interpret the coefficient of determination.
Question
Advertising and Money Spent Narrative
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Does a linear relationship exist between x and y? Test using
= 0.05.
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Does a linear relationship exist between x and y? Test using
= 0.05. Question
Correlation between Shoreline Erosion and Rainfall
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below. s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%
Analysis of Variance
Refer to Correlation between Shoreline Erosion and Rainfall. What is the equation of the estimated regression line?
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below.
s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%Analysis of Variance
Refer to Correlation between Shoreline Erosion and Rainfall. What is the equation of the estimated regression line?
Question
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Predict with 95% confidence the monthly sales of a salesperson with ten years of experience.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Predict with 95% confidence the monthly sales of a salesperson with ten years of experience.
Question
Correlation between Shoreline Erosion and Rainfall
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below. s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%
Analysis of Variance
Refer to Correlation between Shoreline Erosion and Rainfall. Is the simple linear regression model useful for predicting erosion from a given amount of rainfall? Test the following hypotheses.
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below.
s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%Analysis of Variance
Refer to Correlation between Shoreline Erosion and Rainfall. Is the simple linear regression model useful for predicting erosion from a given amount of rainfall? Test the following hypotheses.
Question
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Determine the standard error of estimate and describe what this statistic tells you about the regression line.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Determine the standard error of estimate and describe what this statistic tells you about the regression line.
Question
Advertising and Money Spent Narrative
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. State and interpret the slope.
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. State and interpret the slope.
Question
Correlation between Shoreline Erosion and Rainfall
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below. s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%
Analysis of Variance
Refer to Correlation between Shoreline Erosion and Rainfall. Interpret the estimated slope of the regression line in the previous question.
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below.
s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%Analysis of Variance
Refer to Correlation between Shoreline Erosion and Rainfall. Interpret the estimated slope of the regression line in the previous question.
Question
Wind Velocity and Windmills Narrative
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x. s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%
Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. . What is the value of the error sum of squares?
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x.
s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. . What is the value of the error sum of squares?
Question
Wind Velocity and Windmills Narrative
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x. s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%
Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. What is the least-squares regression line?
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x.
s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. What is the least-squares regression line?
Question
Wind Velocity and Windmills Narrative
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x. s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%
Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. Does a linear relationship exist between x and y? Test using
= 0.05
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x.
s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. Does a linear relationship exist between x and y? Test using
= 0.05 Question
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Determine the coefficient of determination and discuss what its value tells you about the two variables.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Determine the coefficient of determination and discuss what its value tells you about the two variables.
Question
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Predict with 95% confidence the income of an individual with ten years of education.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Predict with 95% confidence the income of an individual with ten years of education.
Question
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same given value of x (ten years) and same confidence level? Why?
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same given value of x (ten years) and same confidence level? Why?
Question
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Calculate the Pearson correlation coefficient. What sign does it have? Why?
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Calculate the Pearson correlation coefficient. What sign does it have? Why?
Question
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Determine the least-squares regression line.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Determine the least-squares regression line.
Question
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate.
Question
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Estimate with 95% confidence the average income of all individuals with ten years of education.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Estimate with 95% confidence the average income of all individuals with ten years of education.
Question
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same given value of x (ten years) and same confidence level? Why?
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same given value of x (ten years) and same confidence level? Why?
Question
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between years of education and income.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between years of education and income.
Question
Amount of Trees and Beavers
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x.
s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%
Analysis of Variance
Refer to Amount of Trees and Beavers. What is the value of the error sum of squares?
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x.
s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%Analysis of Variance
Refer to Amount of Trees and Beavers. What is the value of the error sum of squares?
Question
Amount of Trees and Beavers
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x. s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%
Analysis of Variance
Refer to Amount of Trees and Beavers. Interpret the estimated slope and intercept for this .
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x.
s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%Analysis of Variance
Refer to Amount of Trees and Beavers. Interpret the estimated slope and intercept for this .
Question
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Estimate the monthly sales for a salesperson with 16 years of experience.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Estimate the monthly sales for a salesperson with 16 years of experience.
Question
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Determine the least-squares regression line.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Determine the least-squares regression line.
Question
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Determine the standard error of estimate and describe what this statistic tells you about the regression line.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Determine the standard error of estimate and describe what this statistic tells you about the regression line.
Question
Amount of Trees and Beavers
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x. s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%
Analysis of Variance
Refer to Amount of Trees and Beavers. What are the estimated slope and estimated intercept?
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x.
s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%Analysis of Variance
Refer to Amount of Trees and Beavers. What are the estimated slope and estimated intercept?
Question
Amount of Trees and Beavers
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x. s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%
Analysis of Variance
Refer to Amount of Trees and Beavers. What is the least-squares regression equation?
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x.
s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%Analysis of Variance
Refer to Amount of Trees and Beavers. What is the least-squares regression equation?
Question
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Estimate the income of an individual with 15 years of education.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Estimate the income of an individual with 15 years of education.
Question
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Interpret the value of the slope of the regression line.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Interpret the value of the slope of the regression line.
Question
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate.
Question
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Interpret the value of the slope of the regression line.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Interpret the value of the slope of the regression line.
Question
Age of Forest and Diameter of Trees
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Construct a scatterplot for this data, including the least-squares regression line.
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Construct a scatterplot for this data, including the least-squares regression line.
Question
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Find and interpret the correlation coefficient.
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Find and interpret the correlation coefficient.
Question
Age of Forest and Diameter of Trees
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Is the simple linear regression model useful for predicting the diameter of the trees from a given age of the forest? Use the t-test at
= 0.05.
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Is the simple linear regression model useful for predicting the diameter of the trees from a given age of the forest? Use the t-test at
= 0.05. Question
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. What is the least-squares regression line?
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. What is the least-squares regression line?
Question
Vending Machines Narrative
Let x be the number of vending machines and let y be the time (in hours) it takes to stock them. The data are as follows.
Refer to Vending Machines Narrative. Construct a scatterplot for this data including the least-squares regression line.
Let x be the number of vending machines and let y be the time (in hours) it takes to stock them. The data are as follows.
Refer to Vending Machines Narrative. Construct a scatterplot for this data including the least-squares regression line.
Question
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. What does the scatterplot developed in the previous question indicate about the relationship between the two variables?
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. What does the scatterplot developed in the previous question indicate about the relationship between the two variables?
Question
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Use a statistical software package of your choice and report the regression analysis results.
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Use a statistical software package of your choice and report the regression analysis results.
Question
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Find and interpret the coefficient of determination.
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Find and interpret the coefficient of determination.
Question
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Use the F-test to test the hypotheses
at 
= 0.05.
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Use the F-test to test the hypotheses
at = 0.05. Question
Vending Machines Narrative
Let x be the number of vending machines and let y be the time (in hours) it takes to stock them. The data are as follows.
Refer to Vending Machines Narrative. What is the equation of the estimated regression line?
Let x be the number of vending machines and let y be the time (in hours) it takes to stock them. The data are as follows.
Refer to Vending Machines Narrative. What is the equation of the estimated regression line?
Question
Age of Forest and Diameter of Trees
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. What is the equation of the least-squares regression line?
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. What is the equation of the least-squares regression line?
Question
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Develop a scatterplot for this data.
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Develop a scatterplot for this data.
Question
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Use the t-test to test the hypotheses
.
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Use the t-test to test the hypotheses
. Question
Amount of Trees and Beavers
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x. s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%
Analysis of Variance
Refer to Amount of Trees and Beavers. What is the percentage of variation in beaver abundance accounted for by regression on the density of aspen trees?
NAR: Amount of Trees and Beavers
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x.
s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%Analysis of Variance
Refer to Amount of Trees and Beavers. What is the percentage of variation in beaver abundance accounted for by regression on the density of aspen trees?
NAR: Amount of Trees and Beavers
Question
Vending Machines Narrative
Let x be the number of vending machines and let y be the time (in hours) it takes to stock them. The data are as follows.
Refer to Vending Machines Narrative. Use a software package of your choice and report the regression analysis results.
Let x be the number of vending machines and let y be the time (in hours) it takes to stock them. The data are as follows.
Refer to Vending Machines Narrative. Use a software package of your choice and report the regression analysis results.
Question
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. What is the average change in growth with the increase of one leaf?
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. What is the average change in growth with the increase of one leaf?
Question
Amount of Trees and Beavers
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x. s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%
Analysis of Variance
Refer to Amount of Trees and Beavers. What is the value of the coefficient of determination?
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x.
s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%Analysis of Variance
Refer to Amount of Trees and Beavers. What is the value of the coefficient of determination?
Question
Age of Forest and Diameter of Trees
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Use a statistical software package of your choice and report the regression analysis results.
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Use a statistical software package of your choice and report the regression analysis results.
Question
Age of Forest and Diameter of Trees
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Estimate
using a 90% confidence interval.
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Estimate
using a 90% confidence interval. Question
Age of Forest and Diameter of Trees
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Predict the tree diameter of an 83-year-old forest.
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Predict the tree diameter of an 83-year-old forest.
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Deck 12: B: linear Regression and Correlation
1
Lumber Weight Narrative
Let x be the weight in tonnes (1 tonne = 1000 kg) of a load of lumber and y be the time (in hours) it takes to load it onto a truck. A simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 6.5 and a = 3.3.
Refer to Lumber Weight Narrative. What is the least-squares best-fitting regression line?
Let x be the weight in tonnes (1 tonne = 1000 kg) of a load of lumber and y be the time (in hours) it takes to load it onto a truck. A simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 6.5 and a = 3.3.
Refer to Lumber Weight Narrative. What is the least-squares best-fitting regression line?
= 3.3 + 6.5x 2
Blacktop
Let x be the area (in square metres) to be covered with blacktop, and let y be the time (in minutes) it takes a construction crew to completely cover the area. The simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 0.207 and a = 81.6.
Refer to Blacktop statement. What is the estimated amount of time it takes to apply 2400 square metres of blacktop?
Let x be the area (in square metres) to be covered with blacktop, and let y be the time (in minutes) it takes a construction crew to completely cover the area. The simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 0.207 and a = 81.6.
Refer to Blacktop statement. What is the estimated amount of time it takes to apply 2400 square metres of blacktop?
= 81.6 + 0.207 (2400) = 578.4 minutes 3
Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
Refer to Salary and Years Narrative. Does a linear relationship exist between x and y? Test using = 0.05.
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%Refer to Salary and Years Narrative. Does a linear relationship exist between x and y? Test using
= 0.05.
Since p-value = 0.0 < 
, reject the null hypothesis and conclude that a linear relationship does exist between x and y. 4
Delivery Time Narrative
Let x be the number of pieces of furniture in a delivery truck and y be the time (in hours) it takes the delivery person to deliver all the pieces of furniture. A simple linear regression analysis related x and y where the least-squares estimates of the regression parameters are a = 1.85 and b = 0.55.
Refer to Delivery Time Narrative. Use the least-squares regression line to estimate the time it takes to deliver ten pieces of furniture. (You may assume that ten is in the range of the data.)
Let x be the number of pieces of furniture in a delivery truck and y be the time (in hours) it takes the delivery person to deliver all the pieces of furniture. A simple linear regression analysis related x and y where the least-squares estimates of the regression parameters are a = 1.85 and b = 0.55.
Refer to Delivery Time Narrative. Use the least-squares regression line to estimate the time it takes to deliver ten pieces of furniture. (You may assume that ten is in the range of the data.)
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5
Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
Refer to Salary and Years Narrative. What are the values of and the sum of squares for error?
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%Refer to Salary and Years Narrative. What are the values of
and the sum of squares for error? Unlock Deck
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6
Lumber Weight Narrative
Let x be the weight in tonnes (1 tonne = 1000 kg) of a load of lumber and y be the time (in hours) it takes to load it onto a truck. A simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 6.5 and a = 3.3.
Refer to Lumber Weight Narrative. What is the estimated time it takes to load 9 tonnes of lumber?
Let x be the weight in tonnes (1 tonne = 1000 kg) of a load of lumber and y be the time (in hours) it takes to load it onto a truck. A simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 6.5 and a = 3.3.
Refer to Lumber Weight Narrative. What is the estimated time it takes to load 9 tonnes of lumber?
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7
Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
Refer to Salary and Years Narrative. What is the least-squares regression equation?
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%Refer to Salary and Years Narrative. What is the least-squares regression equation?
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8
Delivery Time Narrative
Let x be the number of pieces of furniture in a delivery truck and y be the time (in hours) it takes the delivery person to deliver all the pieces of furniture. A simple linear regression analysis related x and y where the least-squares estimates of the regression parameters are a = 1.85 and b = 0.55.
Refer to Delivery Time Narrative. Identify and interpret the slope of the equation.
Let x be the number of pieces of furniture in a delivery truck and y be the time (in hours) it takes the delivery person to deliver all the pieces of furniture. A simple linear regression analysis related x and y where the least-squares estimates of the regression parameters are a = 1.85 and b = 0.55.
Refer to Delivery Time Narrative. Identify and interpret the slope of the equation.
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9
Delivery Time Narrative
Let x be the number of pieces of furniture in a delivery truck and y be the time (in hours) it takes the delivery person to deliver all the pieces of furniture. A simple linear regression analysis related x and y where the least-squares estimates of the regression parameters are a = 1.85 and b = 0.55.
Refer to Delivery Time Narrative. Identify and interpret the y-intercept. Does this make sense?
Let x be the number of pieces of furniture in a delivery truck and y be the time (in hours) it takes the delivery person to deliver all the pieces of furniture. A simple linear regression analysis related x and y where the least-squares estimates of the regression parameters are a = 1.85 and b = 0.55.
Refer to Delivery Time Narrative. Identify and interpret the y-intercept. Does this make sense?
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10
Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
Refer to Salary and Years Narrative. What are the least-squares estimates of the slope and the y-intercept?
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%Refer to Salary and Years Narrative. What are the least-squares estimates of the slope and the y-intercept?
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11
Blacktop
Let x be the area (in square metres) to be covered with blacktop, and let y be the time (in minutes) it takes a construction crew to completely cover the area. The simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 0.207 and a = 81.6.
Refer to Blacktop statement. What is the average change in time per one square metre increase in area?
Let x be the area (in square metres) to be covered with blacktop, and let y be the time (in minutes) it takes a construction crew to completely cover the area. The simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 0.207 and a = 81.6.
Refer to Blacktop statement. What is the average change in time per one square metre increase in area?
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12
Lumber Weight Narrative
Let x be the weight in tonnes (1 tonne = 1000 kg) of a load of lumber and y be the time (in hours) it takes to load it onto a truck. A simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 6.5 and a = 3.3.
Refer to Lumber Weight Narrative. What is the average change in time per one tonne increase in weight?
Let x be the weight in tonnes (1 tonne = 1000 kg) of a load of lumber and y be the time (in hours) it takes to load it onto a truck. A simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 6.5 and a = 3.3.
Refer to Lumber Weight Narrative. What is the average change in time per one tonne increase in weight?
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13
Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
Refer to Salary and Years Narrative. Find and interpret the coefficient of determination.
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%Refer to Salary and Years Narrative. Find and interpret the coefficient of determination.
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14
Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
Refer to Salary and Years Narrative. Find and interpret the correlation coefficient.
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%Refer to Salary and Years Narrative. Find and interpret the correlation coefficient.
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15
Advertising and Money Spent Narrative
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Use a statistical software package of your choice and report the regression analysis results.
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Use a statistical software package of your choice and report the regression analysis results.
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16
Lumber Weight Narrative
Let x be the weight in tonnes (1 tonne = 1000 kg) of a load of lumber and y be the time (in hours) it takes to load it onto a truck. A simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 6.5 and a = 3.3.
Refer to Lumber Weight Narrative. Interpret the y-intercept of the regression line.
Let x be the weight in tonnes (1 tonne = 1000 kg) of a load of lumber and y be the time (in hours) it takes to load it onto a truck. A simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 6.5 and a = 3.3.
Refer to Lumber Weight Narrative. Interpret the y-intercept of the regression line.
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17
Delivery Time Narrative
Let x be the number of pieces of furniture in a delivery truck and y be the time (in hours) it takes the delivery person to deliver all the pieces of furniture. A simple linear regression analysis related x and y where the least-squares estimates of the regression parameters are a = 1.85 and b = 0.55.
Refer to Delivery Time Narrative. What is the least-squares best-fitting regression line?
Let x be the number of pieces of furniture in a delivery truck and y be the time (in hours) it takes the delivery person to deliver all the pieces of furniture. A simple linear regression analysis related x and y where the least-squares estimates of the regression parameters are a = 1.85 and b = 0.55.
Refer to Delivery Time Narrative. What is the least-squares best-fitting regression line?
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18
Salary and Years Narrative
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points. s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%
Refer to Salary and Years Narrative. Interpret the estimated slope and y-intercept for this .
A company manager is interested in the relationship between x = number of years that an employee has been with the company and y = the employee's annual salary (in thousands of dollars). The following statistical software output is from a regression analysis for predicting y from x for n = 15 data points.
s = 0.8081 R-sq = 97.9% R-sq(adj) = 97.8%Refer to Salary and Years Narrative. Interpret the estimated slope and y-intercept for this .
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19
Blacktop
Let x be the area (in square metres) to be covered with blacktop, and let y be the time (in minutes) it takes a construction crew to completely cover the area. The simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 0.207 and a = 81.6.
Refer to Blacktop statement. What is the least-squares best-fitting regression line?
Let x be the area (in square metres) to be covered with blacktop, and let y be the time (in minutes) it takes a construction crew to completely cover the area. The simple linear regression model relates x and y where the least-squares estimates of the regression parameters are b = 0.207 and a = 81.6.
Refer to Blacktop statement. What is the least-squares best-fitting regression line?
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20
Advertising and Money Spent Narrative
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Develop a scatterplot and determine whether a linear relationship appears to provide a good fit to this data set.
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Develop a scatterplot and determine whether a linear relationship appears to provide a good fit to this data set.
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21
Advertising and Money Spent Narrative
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. What is the least-squares regression line?
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. What is the least-squares regression line?
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22
Wind Velocity and Windmills Narrative
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x. s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%
Analysis of Variance
-Refer to Wind Velocity and Windmills Narrative. One of the assumptions about the random error in the regression model is that the values of have a common variance equal to . What is the best estimator of ?
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x.
s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%Analysis of Variance
-Refer to Wind Velocity and Windmills Narrative. One of the assumptions about the random error
in the regression model is that the values of have a common variance equal to . What is the best estimator of ? Unlock Deck
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23
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Determine the coefficient of determination and discuss what its value tells you about the two variables.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Determine the coefficient of determination and discuss what its value tells you about the two variables.
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24
Advertising and Money Spent Narrative
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Calculate and SSE for these data.
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Calculate
and SSE for these data. Unlock Deck
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25
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Estimate with 95% confidence the average monthly sales of all salespersons with ten years of experience.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Estimate with 95% confidence the average monthly sales of all salespersons with ten years of experience.
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26
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between years of experience and sales.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between years of experience and sales.
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27
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Calculate the Pearson correlation coefficient. What sign does it have? Why?
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Calculate the Pearson correlation coefficient. What sign does it have? Why?
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28
Wind Velocity and Windmills Narrative
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x. s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%
Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. Predict the DC output for a wind velocity of 22 km/h.
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x.
s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. Predict the DC output for a wind velocity of 22 km/h.
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29
Correlation between Shoreline Erosion and Rainfall
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below. s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%
Analysis of Variance
Refer to Correlation Between Shoreline Erosion and Rainfall. Identify and interpret the coefficient of determination.
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below.
s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%Analysis of Variance
Refer to Correlation Between Shoreline Erosion and Rainfall. Identify and interpret the coefficient of determination.
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30
Wind Velocity and Windmills Narrative
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x. s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%
Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. . Identify and interpret the coefficient of determination.
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x.
s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. . Identify and interpret the coefficient of determination.
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31
Advertising and Money Spent Narrative
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Does a linear relationship exist between x and y? Test using = 0.05.
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. Does a linear relationship exist between x and y? Test using
= 0.05. Unlock Deck
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32
Correlation between Shoreline Erosion and Rainfall
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below. s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%
Analysis of Variance
Refer to Correlation between Shoreline Erosion and Rainfall. What is the equation of the estimated regression line?
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below.
s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%Analysis of Variance
Refer to Correlation between Shoreline Erosion and Rainfall. What is the equation of the estimated regression line?
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33
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Predict with 95% confidence the monthly sales of a salesperson with ten years of experience.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Predict with 95% confidence the monthly sales of a salesperson with ten years of experience.
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34
Correlation between Shoreline Erosion and Rainfall
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below. s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%
Analysis of Variance
Refer to Correlation between Shoreline Erosion and Rainfall. Is the simple linear regression model useful for predicting erosion from a given amount of rainfall? Test the following hypotheses.
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below.
s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%Analysis of Variance
Refer to Correlation between Shoreline Erosion and Rainfall. Is the simple linear regression model useful for predicting erosion from a given amount of rainfall? Test the following hypotheses.
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35
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Determine the standard error of estimate and describe what this statistic tells you about the regression line.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Determine the standard error of estimate and describe what this statistic tells you about the regression line.
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36
Advertising and Money Spent Narrative
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. State and interpret the slope.
A marketing analyst is studying the relationship between x = money spent on television advertising and y = increase in sales. One study reported the following data (in dollars) for a particular company.
Refer to Advertising and Money Spent Narrative. State and interpret the slope.
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37
Correlation between Shoreline Erosion and Rainfall
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below. s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%
Analysis of Variance
Refer to Correlation between Shoreline Erosion and Rainfall. Interpret the estimated slope of the regression line in the previous question.
A scientist is studying the relationship between x = centimetres of annual rainfall and y = centimetres of shoreline erosion. One study reported the following data. Use the following statistical software output to answer the questions below.
s = 0.2416 R-sq = 98.8% R-sq(adj) = 98.6%Analysis of Variance
Refer to Correlation between Shoreline Erosion and Rainfall. Interpret the estimated slope of the regression line in the previous question.
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38
Wind Velocity and Windmills Narrative
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x. s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%
Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. . What is the value of the error sum of squares?
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x.
s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. . What is the value of the error sum of squares?
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39
Wind Velocity and Windmills Narrative
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x. s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%
Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. What is the least-squares regression line?
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x.
s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. What is the least-squares regression line?
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40
Wind Velocity and Windmills Narrative
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x. s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%
Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. Does a linear relationship exist between x and y? Test using = 0.05
A scientist is studying the relationship between wind velocity (x in km/h) and DC output of a windmill (y). The following MINITAB output is from a regression analysis for predicting y from x.
s = 0.2435 R-sq = 88.3% R-sq(adj) = 87.3%Analysis of Variance
Refer to Wind Velocity and Windmills Narrative. Does a linear relationship exist between x and y? Test using
= 0.05 Unlock Deck
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41
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Determine the coefficient of determination and discuss what its value tells you about the two variables.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Determine the coefficient of determination and discuss what its value tells you about the two variables.
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42
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Predict with 95% confidence the income of an individual with ten years of education.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Predict with 95% confidence the income of an individual with ten years of education.
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43
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same given value of x (ten years) and same confidence level? Why?
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same given value of x (ten years) and same confidence level? Why?
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44
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Calculate the Pearson correlation coefficient. What sign does it have? Why?
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Calculate the Pearson correlation coefficient. What sign does it have? Why?
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45
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Determine the least-squares regression line.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Determine the least-squares regression line.
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46
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate.
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47
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Estimate with 95% confidence the average income of all individuals with ten years of education.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Estimate with 95% confidence the average income of all individuals with ten years of education.
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48
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same given value of x (ten years) and same confidence level? Why?
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same given value of x (ten years) and same confidence level? Why?
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Unlock for access to all 171 flashcards in this deck.
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49
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between years of education and income.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Conduct a test of the population slope to determine at the 5% significance level whether a linear relationship exists between years of education and income.
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50
Amount of Trees and Beavers
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x. s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%
Analysis of Variance
Refer to Amount of Trees and Beavers. What is the value of the error sum of squares?
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x.
s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%Analysis of Variance
Refer to Amount of Trees and Beavers. What is the value of the error sum of squares?
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51
Amount of Trees and Beavers
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x. s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%
Analysis of Variance
Refer to Amount of Trees and Beavers. Interpret the estimated slope and intercept for this .
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x.
s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%Analysis of Variance
Refer to Amount of Trees and Beavers. Interpret the estimated slope and intercept for this .
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52
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Estimate the monthly sales for a salesperson with 16 years of experience.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Estimate the monthly sales for a salesperson with 16 years of experience.
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53
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Determine the least-squares regression line.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Determine the least-squares regression line.
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54
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Determine the standard error of estimate and describe what this statistic tells you about the regression line.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Determine the standard error of estimate and describe what this statistic tells you about the regression line.
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55
Amount of Trees and Beavers
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x. s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%
Analysis of Variance
Refer to Amount of Trees and Beavers. What are the estimated slope and estimated intercept?
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x.
s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%Analysis of Variance
Refer to Amount of Trees and Beavers. What are the estimated slope and estimated intercept?
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56
Amount of Trees and Beavers
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x. s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%
Analysis of Variance
Refer to Amount of Trees and Beavers. What is the least-squares regression equation?
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x.
s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%Analysis of Variance
Refer to Amount of Trees and Beavers. What is the least-squares regression equation?
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57
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Estimate the income of an individual with 15 years of education.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Estimate the income of an individual with 15 years of education.
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58
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Interpret the value of the slope of the regression line.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Interpret the value of the slope of the regression line.
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59
Sales and Experience Narrative
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate.
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1000s) and the years of experience of ten randomly selected salespeople. These data are listed below.
Refer to Sales and Experience Narrative. Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate.
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60
Income and Education Narrative
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Interpret the value of the slope of the regression line.
A professor of economics wants to study the relationship between income (y in $1,000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.
Refer to Income and Education Narrative. Interpret the value of the slope of the regression line.
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61
Age of Forest and Diameter of Trees
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Construct a scatterplot for this data, including the least-squares regression line.
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Construct a scatterplot for this data, including the least-squares regression line.
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62
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Find and interpret the correlation coefficient.
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Find and interpret the correlation coefficient.
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63
Age of Forest and Diameter of Trees
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Is the simple linear regression model useful for predicting the diameter of the trees from a given age of the forest? Use the t-test at = 0.05.
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Is the simple linear regression model useful for predicting the diameter of the trees from a given age of the forest? Use the t-test at
= 0.05. Unlock Deck
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64
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. What is the least-squares regression line?
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. What is the least-squares regression line?
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65
Vending Machines Narrative
Let x be the number of vending machines and let y be the time (in hours) it takes to stock them. The data are as follows.
Refer to Vending Machines Narrative. Construct a scatterplot for this data including the least-squares regression line.
Let x be the number of vending machines and let y be the time (in hours) it takes to stock them. The data are as follows.
Refer to Vending Machines Narrative. Construct a scatterplot for this data including the least-squares regression line.
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66
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. What does the scatterplot developed in the previous question indicate about the relationship between the two variables?
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. What does the scatterplot developed in the previous question indicate about the relationship between the two variables?
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67
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Use a statistical software package of your choice and report the regression analysis results.
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Use a statistical software package of your choice and report the regression analysis results.
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68
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Find and interpret the coefficient of determination.
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Find and interpret the coefficient of determination.
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69
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Use the F-test to test the hypotheses at = 0.05.
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Use the F-test to test the hypotheses
at = 0.05. Unlock Deck
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70
Vending Machines Narrative
Let x be the number of vending machines and let y be the time (in hours) it takes to stock them. The data are as follows.
Refer to Vending Machines Narrative. What is the equation of the estimated regression line?
Let x be the number of vending machines and let y be the time (in hours) it takes to stock them. The data are as follows.
Refer to Vending Machines Narrative. What is the equation of the estimated regression line?
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71
Age of Forest and Diameter of Trees
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. What is the equation of the least-squares regression line?
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. What is the equation of the least-squares regression line?
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72
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Develop a scatterplot for this data.
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Develop a scatterplot for this data.
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73
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Use the t-test to test the hypotheses .
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. Use the t-test to test the hypotheses
. Unlock Deck
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74
Amount of Trees and Beavers
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x. s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%
Analysis of Variance
Refer to Amount of Trees and Beavers. What is the percentage of variation in beaver abundance accounted for by regression on the density of aspen trees?
NAR: Amount of Trees and Beavers
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x.
s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%Analysis of Variance
Refer to Amount of Trees and Beavers. What is the percentage of variation in beaver abundance accounted for by regression on the density of aspen trees?
NAR: Amount of Trees and Beavers
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75
Vending Machines Narrative
Let x be the number of vending machines and let y be the time (in hours) it takes to stock them. The data are as follows.
Refer to Vending Machines Narrative. Use a software package of your choice and report the regression analysis results.
Let x be the number of vending machines and let y be the time (in hours) it takes to stock them. The data are as follows.
Refer to Vending Machines Narrative. Use a software package of your choice and report the regression analysis results.
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76
Young Aspen Trees and Growth Narrative
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. What is the average change in growth with the increase of one leaf?
Let x be the number of leaves on a young aspen tree and let y be the growth of the tree (in mm). The data are as follows.
Refer to Young Aspen Trees and Growth Narrative. What is the average change in growth with the increase of one leaf?
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77
Amount of Trees and Beavers
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x. s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%
Analysis of Variance
Refer to Amount of Trees and Beavers. What is the value of the coefficient of determination?
A scientist is studying the relationship between x = density (in number per square metre) of aspen trees around a pond and y = beaver abundance. The following statistical software output is from a regression analysis for predicting y from x.
s = 0.4839 R-sq = 97.0% R-sq(adj) = 96.5%Analysis of Variance
Refer to Amount of Trees and Beavers. What is the value of the coefficient of determination?
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78
Age of Forest and Diameter of Trees
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Use a statistical software package of your choice and report the regression analysis results.
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Use a statistical software package of your choice and report the regression analysis results.
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79
Age of Forest and Diameter of Trees
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Estimate using a 90% confidence interval.
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Estimate
using a 90% confidence interval. Unlock Deck
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80
Age of Forest and Diameter of Trees
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Predict the tree diameter of an 83-year-old forest.
A scientist is studying the relationship between age of a forest, x, in years and the average diameter of the trees, y, in cm. One study reported the following data.
Refer to Age of Forest and Diameter of Trees. Predict the tree diameter of an 83-year-old forest.
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Unlock Deck
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