Exam 16: Simple Linear Regression and Correlation

If the coefficient of determination is 0.95,this means that 95% of the y values were predicted correctly by the regression line.

Marc Anthony Concert At a recent Marc Anthony concert,a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year.The following data were collected: An Excel output follows: ​ ​ -{Marc Anthony Concert Narrative} Use the regression equation to determine the predicted values of y.

If the standard error of estimate sε = 20 and n = 10,then the sum of squares for error,SSE,is:

Sales and Experience The general manager of a chain of department 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 $1,000s) and the years of experience of 10 randomly selected salespeople. These data are listed below. -{Sales and Experience Narrative} Estimate with 95% confidence the average monthly sales of all salespersons with 10 years of experience.

In a simple linear regression model b₀ is the ____________________ of the straight line.

A zero population correlation coefficient for x and y means that there is no type of relationship whatsoever between x and y.

Sales and Experience The general manager of a chain of department 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 $1,000s)and the years of experience of 10 randomly selected salespeople.These data are listed below. ​ ​ -{Sales and Experience Narrative} Interpret the value of the slope of the regression line.

Income and Education A professor of economics wants to study the relationship between income (y in $1000s)and education (x in years).A random sample eight individuals is taken and the results are shown below. ​ ​ -{Income and Education Narrative} Estimate the income of an individual with 15 years of education.

For a regression analysis to be valid,the error variable must have a standard deviation that is ____________________ regardless of the value of x.

When the error variable does not have constant variance,this condition is called ____________________.

Oil Quality and Price Quality of oil is measured in API gravity degrees--the higher the degrees API,the higher the quality.The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel. A partial Minitab output follows: Descriptive Statistics Variable N Mean StDev SE Mean Degrees 13 34.60 4.613 1.280 Price 13 12.730 0.457 0.127 Covariances Degrees Price Degrees 21.281667 Price 2.026750 0.208833 Regression Analysis Predictor Coef StDev T P Constant 9.4349 0.2867 32.91 0.000 Degrees 0.095235 0.008220 11.59 0.000 S = 0.1314 R−Sq = 92.46% R−Sq(adj)= 91.7% Analysis of Variance Source DF SS MS F P Regression 1 2.3162 2.3162 134.24 0.000 Residual Error 11 0.1898 0.0173 Total 12 2.5060 -{Oil Quality and Price Narrative} Does it appear that the errors are normally distributed? Explain.

Which of the following assumptions concerning the probability distribution of the random error term is stated incorrectly?

If the plot of the residuals is fan shaped,which assumption of regression analysis (if any)is violated?

Marc Anthony Concert At a recent Marc Anthony concert,a survey was conducted that asked a random sample of 20 people their age and how many concerts they have attended since the first of the year.The following data were collected: An Excel output follows: ​ ​ -{Marc Anthony Concert Narrative} Plot the residuals against the predicted values .

If the error variable ε is normally distributed,the test statistic for testing H₀: β₁ = 0 has a Student t-distribution with n − 2 degrees of freedom.

U V's and Skin Cancer A medical statistician wanted to examine the relationship between the amount of UV's (x)and incidence of skin cancer (y).As an experiment he found the number of skin cancers detected per 100,000 of population and the average daily sunshine in eight states around the country.These data are shown below. ​ ​ -{UV's and Skin Cancer Narrative} Calculate the standard error of estimate,and describe what this statistic tells you about the regression line.

In simple linear regression,the coefficient of correlation r and the least squares estimate b₁ of the population slope β₁:

Telemarketing Sales and Experience The general manager of a telemarketing company believes that experience is the most important factor in determining the level of success of a telemarketer.To examine this belief she records last month's sales (in $1,000s)and the years of experience of 10 randomly selected telemarketers.These data are listed below. ​ ​ -{Telemarketer Sales and Experience Narrative} Identify possible outliers.

The coefficient of determination is equal to the coefficient of correlation squared.

Oil Quality and Price Quality of oil is measured in API gravity degrees--the higher the degrees API,the higher the quality.The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel. A partial Minitab output follows: ​ ​ ​ -{Oil Quality and Price Narrative} Plot the least squares regression line on the scatter diagram.