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File: ch12, Chapter 12: Simple Regression Analysis and Correlation True/False 1. If the coefficient of correlation between two numerical variables is -1, it means that the two variables are not related. Ans: False Response: See section 12.1 Correlation Difficulty: Medium 2. The process of constructing a mathematical model to predict or determine one variable by another is called a regression analysis. Ans: True Response: See section 12.2 Introduction to Simple Regression Analysis Difficulty: Easy 3. In simple regression the variable to be predicted is called the predictor variable. Ans: False Response: See section 12.2 Introduction to Simple Regression Analysis Difficulty: Easy 4. In a simple regression analysis the predictor variable is called the independent or explanatory variable. Ans: True Response: See section 12.2 Introduction to Simple Regression Analysis Difficulty: Easy 5. Usually, the first step in regression analysis is to construct a scatter plot. Ans: True Response: See section 12.2 Introduction to Simple Regression Analysis Difficulty: Medium 6. Data points that are apart from the rest of the points in a data set used in a regression analysis are called extraordinary observations. Ans: False Response: See section 12.4 Residual Analysis Difficulty: Medium 7. The sum of the residuals in any given regression analysis is always zero. Ans: True Response: See section 12.4 Residual Analysis Difficulty: Medium 8. A linear regression model analysis assumes that the error terms are independent, normally distributed and have the non-constant variances. Ans: False Response: See section 12.4 Residual Analysis Difficulty: Hard 9. The numerical value of the coefficient of determination r2 varies from –1 to +1. Ans: False Response: See section 12.6 Coefficient of Determination Difficulty: Medium 10. If a regression model has an r2 of 0.20, it means that about 20% of the variation in the dependent variable is explained by the regression model. Ans: True Response: See section 12.6 Coefficient of Determination Difficulty: Medium 11. In simple regression estimation, the confidence interval is always wider than the prediction interval. Ans: False Response: See section 12.8 Estimation Difficulty: Hard Multiple Choice 12. A value of -1 for the coefficient of correlation between two variables means that the two variables are ________________. a) not related at all b) very weakly related c) weakly related d) somewhat strongly related e) perfectly related Ans: e Response: See section 12.1 Correlation Difficulty: Hard 13. The following regression model was fitted to sample data with 12 observations: ŷ = 30 + 4.50x. What is the change in the predicted value of y for a unit change in the value? a) 30 b) 43.40 c) 4.50 d) 36 e) 57.00 Ans: c Response: See section 12.3 Determining the Equation of the Regression Line Difficulty: Medium 14. The following regression model was fitted to sample data with 12 observations: ŷ = 30 + 4.50x. What is the predicted value of y for a given value of x = 6? a) 30 b) 43.40 c) 4.50 d) 36 e) 57.00 Ans: e Response: See section 12.4 Residual Analysis Difficulty: Medium 15. The following regression model was fitted to sample data with 12 observations: ŷ = 30 + 4.50x. What is the residual for an observation (x = 2, y = 40)? a) 0 b) 1 c) 0.50 d) -0.50 e) -1 Ans: b Response: See section 12.4 Residual Analysis Difficulty: Medium 16. Which of the following is not an assumption of the regression model? a) The model is linear b) The error terms decrease as x values increase c) The error terms are normally distributed d) The error terms are independent e) The error terms have constant variance Ans: b Response: See section 12.4 Residual Analysis Difficulty: Medium 17. If the error variances of a regression model are not constant, it is called _________. a) heteroscedasticity b) homoscedasticity c) nonlinearity d) non independent error terms e) multicollinearity Ans: a Response: See section 12.4 Residual Analysis Difficulty: Medium 18. If the sum of squares of error for a simple regression model fitted for twelve pairs of observations is 250, what is the standard error of the estimate for the model? a) 4.00 b) 4.56 c) 4.77 d) 5.00 e) 5.07 Ans: d Response: See section 12.5 Standard Error of the Estimate Difficulty: Medium 19. If the standard error of the estimate for a regression model fitted to a large number of paired observations is 1.75, approximately 68% of the residuals would lie within ______ a) −0.68 and +0.68 b) −0.95 and +0.95 c) −0.97 and +0.97 d) −1.75 and +1.75 e) −3.50 and +3.50 Ans: d Response: See section 12.5 Standard Error of the Estimate Difficulty: Medium 20. Some entries have been deleted from the following analysis of variance table that is part of the computer output from a simple regression analysis of a data set containing 11 matched-pair observations. Source Regression Residual Total df 1 SS 11 19222.72 MS 9315.23 F p-Value 0.017340862 Based on this output, what is the value of the mean square error? a) 33.18 b) 990.749 c) 9315.23 d) 1100.83 e) 8.4619 Ans: b Response: See section 12.7 Hypothesis Tests for the Slope of the Regression Model and Testing the Overall Model Difficulty: Hard 21. Some entries have been deleted from the following analysis of variance table that is part of the computer output from a simple regression analysis of a data set containing 11 matched-pair observations. Source Regression Residual Total df 1 SS 11 19222.72 MS 9315.23 F p-Value 0.01734 Based on this output, what is the value of the F statistic? a) 33.18 b) 9907.49 c) 9315.23 d) 1100.83 e) 9.4022 Ans: e Response: See section 12.7 Hypothesis Tests for the Slope of the Regression Model and Testing the Overall Model Difficulty: Hard 22. Some entries have been deleted from the following analysis of variance table that is part of the computer output from a simple regression analysis of a data set containing 11 matched-pair observations. Source Regression Residual Total df 1 SS 9315.23 11 19222.72 MS 9315.23 F Based on this output, what is the value of the standard error of estimate? a) 31.48 b) 9907.49 c) 9315.23 d) 1100.83 e) 8.4619 Ans: a Response: See section 12.5 Standard Error of the Estimate Difficulty: Hard p-Value 0.01734