Exam 14: Introduction to Linear Regression and Correlation Analysis

Assume that you have calculated a prediction of = 110 where the specific value for x is equal to the average value of x.Also assume that n = 201 and that the standard error of the estimate is s_ε = 4.5.Find the approximate 95 percent prediction interval.

(Multiple Choice)

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Question 41

When the intercept in a regression equation is deemed not significantly different from 0,then in making predictions for y,0.0 should be used as the value of the intercept rather than the estimated intercept value.

(True/False)

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Question 42

Which of the following statements is true with respect to a simple linear regression model?

(Multiple Choice)

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Question 43

A correlation of -0.9 indicates a weak linear relationship between the variables.

(True/False)

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Question 44

If two variables are highly correlated,it not only means that they are linearly related,it also means that a change in one variable will cause a change in the other variable.

(True/False)

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Question 45

Both a scatter plot and the correlation coefficient can distinguish between a curvilinear and a linear relationship.

(True/False)

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Question 46

If the correlation coefficient for two variables is computed to be a -0.70,the scatter plot will show the data to be downward sloping from left to right.

(True/False)

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Question 47

In simple linear regression,the t-test for the slope and the F-test are both conducting the same hypothesis test.

(True/False)

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Question 48

A perfect correlation between two variables will always produce a correlation coefficient of +1.0.

(True/False)

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Question 49

A high coefficient of determination (R²)implies that the regression model will be a good predictor for future values of the dependent variable given the value of the independent variable.

(True/False)

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Question 50

You are given the following sample data for two variables: Based upon these sample data,and testing at the 0.05 level of significance,the critical value for testing whether the population correlation coefficient is equal to zero is t = 2.2622.

(True/False)

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Question 51

Given the following regression equation,the predicted value for y when x = 0.5 is about 4.57. ANOVA

(True/False)

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Question 52

Given a sample of size n = 15 and a sample correlation of r = 0.7,the value of the test statistic for conducting a hypothesis test of the correlation is t = 3.53.

(True/False)

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Question 53

Explain what the correlation coefficient measures and some detail of the key issues associated with it.Be sure to also discuss the concept of spurious correlation.

(Essay)

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Question 54

Given a regression equation of = 16 + 2.3x we would expect that an increase in x of 2.0 would lead to an average increase of y of 4.6.

(True/False)

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Question 55

If the correlation between two variables is known to be statistically significant at the 0.05 level,then the regression slope coefficient will also be significant at the 0.05 level.

(True/False)

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Question 56

If the R-square value for a simple linear regression model is .80,the correlation between the two variables is known to be .64.

(True/False)

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Question 57

In conducting a hypothesis test for a correlation,the correct probability distribution to use is the F distribution.

(True/False)

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Question 58

You are given the following sample data for two variables: The sample correlation coefficient for these data is approximately r = 0.755.

(True/False)

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Question 59

If a simple least squares regression model is developed based on sample where the two variables are known to be positively correlated,the sum of the residuals will be positive.

(True/False)

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Question 60

Showing 41 - 60 of 136

Assume that you have calculated a prediction of = 110 where the specific value for x is equal to the average value of x.Also assume that n = 201 and that the standard error of the estimate is s_ε = 4.5.Find the approximate 95 percent prediction interval.

When the intercept in a regression equation is deemed not significantly different from 0,then in making predictions for y,0.0 should be used as the value of the intercept rather than the estimated intercept value.

Which of the following statements is true with respect to a simple linear regression model?

A correlation of -0.9 indicates a weak linear relationship between the variables.

If two variables are highly correlated,it not only means that they are linearly related,it also means that a change in one variable will cause a change in the other variable.

Both a scatter plot and the correlation coefficient can distinguish between a curvilinear and a linear relationship.

If the correlation coefficient for two variables is computed to be a -0.70,the scatter plot will show the data to be downward sloping from left to right.

In simple linear regression,the t-test for the slope and the F-test are both conducting the same hypothesis test.

A perfect correlation between two variables will always produce a correlation coefficient of +1.0.

A high coefficient of determination (R²)implies that the regression model will be a good predictor for future values of the dependent variable given the value of the independent variable.

You are given the following sample data for two variables: Based upon these sample data,and testing at the 0.05 level of significance,the critical value for testing whether the population correlation coefficient is equal to zero is t = 2.2622.

Given the following regression equation,the predicted value for y when x = 0.5 is about 4.57. ANOVA

Given a sample of size n = 15 and a sample correlation of r = 0.7,the value of the test statistic for conducting a hypothesis test of the correlation is t = 3.53.

Explain what the correlation coefficient measures and some detail of the key issues associated with it.Be sure to also discuss the concept of spurious correlation.

Given a regression equation of = 16 + 2.3x we would expect that an increase in x of 2.0 would lead to an average increase of y of 4.6.

If the correlation between two variables is known to be statistically significant at the 0.05 level,then the regression slope coefficient will also be significant at the 0.05 level.

If the R-square value for a simple linear regression model is .80,the correlation between the two variables is known to be .64.

In conducting a hypothesis test for a correlation,the correct probability distribution to use is the F distribution.

You are given the following sample data for two variables: The sample correlation coefficient for these data is approximately r = 0.755.

If a simple least squares regression model is developed based on sample where the two variables are known to be positively correlated,the sum of the residuals will be positive.

The Where, why, and How of Data Collection

Graphs,charts and Tablesdescribing Your Data

Describing Data Using Numerical Measures

Using Probability and Probability Distributions

Discrete Probability Distributions

Introduction to Continuous Probability Distributions

Introduction to Sampling Distributions

Estimating Single Population Parameters

Introduction to Hypothesis Testing

Estimation and Hypothesis Testing for Two Population Parameters

Hypothesis Tests and Estimation for Population Variances

Analysis of Variance

Goodness-Of-Fit Tests and Contingency Analysis

Multiple Regression Analysis and Model Building

Analyzing and Forecasting Time-Series Data

Introduction to Nonparametric Statistics

Introduction to Quality and Statistical Process Control

Introduction to Decision Analysis

Filters

Exam 14: Introduction to Linear Regression and Correlation Analysis

Assume that you have calculated a prediction of = 110 where the specific value for x is equal to the average value of x.Also assume that n = 201 and that the standard error of the estimate is sε = 4.5.Find the approximate 95 percent prediction interval.

When the intercept in a regression equation is deemed not significantly different from 0,then in making predictions for y,0.0 should be used as the value of the intercept rather than the estimated intercept value.

Which of the following statements is true with respect to a simple linear regression model?

A correlation of -0.9 indicates a weak linear relationship between the variables.

If two variables are highly correlated,it not only means that they are linearly related,it also means that a change in one variable will cause a change in the other variable.

Both a scatter plot and the correlation coefficient can distinguish between a curvilinear and a linear relationship.

If the correlation coefficient for two variables is computed to be a -0.70,the scatter plot will show the data to be downward sloping from left to right.

In simple linear regression,the t-test for the slope and the F-test are both conducting the same hypothesis test.

A perfect correlation between two variables will always produce a correlation coefficient of +1.0.

A high coefficient of determination (R2)implies that the regression model will be a good predictor for future values of the dependent variable given the value of the independent variable.

You are given the following sample data for two variables: Based upon these sample data,and testing at the 0.05 level of significance,the critical value for testing whether the population correlation coefficient is equal to zero is t = 2.2622.

Given the following regression equation,the predicted value for y when x = 0.5 is about 4.57. ANOVA

Given a sample of size n = 15 and a sample correlation of r = 0.7,the value of the test statistic for conducting a hypothesis test of the correlation is t = 3.53.

Explain what the correlation coefficient measures and some detail of the key issues associated with it.Be sure to also discuss the concept of spurious correlation.

Given a regression equation of = 16 + 2.3x we would expect that an increase in x of 2.0 would lead to an average increase of y of 4.6.

If the correlation between two variables is known to be statistically significant at the 0.05 level,then the regression slope coefficient will also be significant at the 0.05 level.

If the R-square value for a simple linear regression model is .80,the correlation between the two variables is known to be .64.

In conducting a hypothesis test for a correlation,the correct probability distribution to use is the F distribution.

You are given the following sample data for two variables: The sample correlation coefficient for these data is approximately r = 0.755.

If a simple least squares regression model is developed based on sample where the two variables are known to be positively correlated,the sum of the residuals will be positive.

The Where, why, and How of Data Collection

Graphs,charts and Tablesdescribing Your Data

Describing Data Using Numerical Measures

Using Probability and Probability Distributions

Discrete Probability Distributions

Introduction to Continuous Probability Distributions

Introduction to Sampling Distributions

Estimating Single Population Parameters

Introduction to Hypothesis Testing

Estimation and Hypothesis Testing for Two Population Parameters

Hypothesis Tests and Estimation for Population Variances

Analysis of Variance

Goodness-Of-Fit Tests and Contingency Analysis

Multiple Regression Analysis and Model Building

Analyzing and Forecasting Time-Series Data

Introduction to Nonparametric Statistics

Introduction to Quality and Statistical Process Control

Introduction to Decision Analysis

Filters

Assume that you have calculated a prediction of = 110 where the specific value for x is equal to the average value of x.Also assume that n = 201 and that the standard error of the estimate is s_ε = 4.5.Find the approximate 95 percent prediction interval.

A high coefficient of determination (R²)implies that the regression model will be a good predictor for future values of the dependent variable given the value of the independent variable.