# In a regression model involving 50 observations, the following

1. In a regression model involving 50 observations, the following estimated regression model was obtained:

yˆ=10.5+3.2×1+5.8×2+6.5×3
For this model, SSR=450 and SSE=175. The value of the MSR is:
A. 150
B. 3.804
C. 12.50
D. 275

2. In multiple regression analysis involving 10 independent variables and 100 observations, the critical value t for testing individual coefficients in the model will have:
A. 100 degrees of freedom
B. 10 degrees of freedom
C. 9 degrees of freedom
D. 89 degrees of freedom

3. A multiple regression analysis involving 3 independent variables and 25 data points results in a value of 0.769 for the unadjusted multiple coefficient of determination. The adjusted multiple coefficient of determination is:
A. 0.385
B. 0.877
C. 0.591
D. 0.736

4. Which of the following is not true when we add an independent variable to a multiple regression model?
A. The unadjusted coefficient of determination always increases
B. The unadjusted coefficient of determination may increase or decrease
C. The adjusted coefficient of determination can assume a negative value
D. The adjusted coefficient of determination may increase

5. In a multiple regression model, the standard deviation of the error variable ϵ is assumed to be:
A. constant for all values of the independent variables
B. not enough information is given to answer this question
C. 1.0
D. constant for all values of the dependent variables

6. In multiple regression, the mean of the probability distribution of the error variable ϵ is assumed to be:
A. 0.0
B. 1.0
C. k,where k is the number of independent variables included in the model
D. Any value greater than 1

7. In multiple regression analysis, even when there is no linear relationship between any of the independent variables and the dependent variable, then
A. the chance of erroneously concluding that the model is useful is substantially less with the F−test than with multiple t−tests
B. multiple t−tests of the individual coefficients may still show that some are significant
C. we may conclude erroneously that the model has some validity
D. all of the above statements are correct

8. A multiple regression model has the form

yˆ=8+3×1+5×2−4×3

As x3 increases by 1 unit, with x1 and x2 held constant, then y, on average, is expected to:
A. increase by 1 unit
B. decrease by 16 units
C. increase by 12 units
D. decrease by 4 units