# Multiple regression analysis

T F 1. Multiple regression analysis is used when one independent variable is used to predict values of two or more dependent variables.

T F 2. A net regression coefficient, b3, indicates the change in the predicted value for a unit change in X3 when all other Xi variables are held constant.

T F 3. Multiple regression analysis examines the relationship of several dependent variables on the independent variable.

T F 4. The coefficient of multiple determination reports the strength of the association between a dependent variable and a set of independent variables.

T F 5. Multiple R2 measures the proportion of explained variation relative to total variation.

T F 6. A correlation matrix shows individual correlation coefficients for all pairs of variables.

T F 7. A dummy variable is added to the regression equation to control for error.

8. In multiple regression analysis, residual analysis is used to test the requirement that
A) the variation in the residuals is the same for all fitted values of Y`
B) the independent variables are the direct cause of the dependent variable
C) the number of independent variables included in the analysis is correct
D) prediction error is minimized

9. How is the degree of association between a set of independent variables and a dependent variable measured?
A) Confidence intervals.
B) Autocorrelation
C) Coefficient of multiple determination
D) Standard error of estimate

10. In a multiple regression ANOVA table, explained variation is represented by
A) the regression sum of squares
B) the total sum of squares
C) the regression coefficients
D) the correlation matrix

11. If the coefficient of multiple determination is 0.81, what percent of variation is not explained?
A) 19%
B) 90%
C) 66%
D) 81%

12. In multiple regression analysis, testing the global null hypothesis that the multiple regression coefficients are all zero is based on
A) a z statistic
B) a t statistic
C) a F statistic
D) binomial distribution

13. In the general multiple regression equation which of the following variables represents the Y intercept?
A) b1
B) x1
C) Y`
D) a

14. What can we conclude if the net regression coefficients in the population are not significantly different from zero?
A) A strong relationship exists among the variables
B) No relationship exists between the dependent variable and any of the independent variables
C) The independent variables are good predictors
D) Good forecasts are possible

15. Which of the following is a characteristic of the F-distribution?
A) Normally distributed
B) Positively skewed
C) Negatively skewed
D) Equal to the t-distribution

16. In a regression analysis, three independent variables are used in the equation based on a sample of forty observations. What are the degrees of freedom associated with the F-statistic?
A) 3 and 39
B) 4 and 40
C) 3 and 36
D) 2 and 39

17. Which statistic tests hypotheses about individual regression coefficients?
A) t-statistic
B) z-statistic
C) X2 (chi-square statistic)
D) F

18. The coefficient of determination measures the proportion of
A) explained variation relative to total variation.
B) variation due to the relationship among variables.
C) error variation relative to total variation.
D) variation due to regression.

19. For a unit change in X1 holding X2 constant, what change can be expected in the dependent variable
in the multiple regression equation Y’ = 5.2 + 6.3X1 – 7.1X2?
A) – 7.1
B) + 6.3
C) + 5.2
D) + 4.4

20. The best example of a null hypothesis for a global test of a multiple regression model is:
A) Ho:β1= β2= β3= β4
B) Ho:µ1=µ2=µ3=µ4
C) Ho:β1= 0
D) If F is greater than 20.00 then reject

Use the following to answer questions 21-24:

The following correlations were computed as part of a multiple regression analysis that used education,
job, and age to predict income.
Income Education Job Age
Income 1.000
Education 0.677 1.000
Job 0.173 -0.181 1.000
Age 0.369 0.073 0.689 1.00

21. What is this table called?
A) Net regression coefficients
B) Coefficients of nondetermination
C) Analysis of variance
D) Correlation matrix

22. Which is the dependent variable?
A) Income
B) Age
C) Education
D) Job

23. Which independent variable has the strongest association with the dependent variable?
A) Income
B) Age
C) Education
D) Job

24. Which independent variable has the weakest association with the dependent variable?
A) Income
B) Age
C) Education
D) Job

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