Download File: ch13, Chapter 13: Multiple Regression Analysis True/False 1

File: ch13, Chapter 13: Multiple Regression Analysis
True/False
1. The process of constructing a mathematical model to predict or determine one variable by two
or more explanatory variables is called a compound regression analysis.
Ans: False
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
2. In multiple simple regression analysis the dependent variable is sometimes referred to as the
response variable.
Ans6: True
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
3. Unlike a simple regression model which has one dependent variable, a multiple regression
model has more than one dependent variable.
Ans: False
Response: See section 13.1 The Multiple Regression Model
Difficulty: Easy
4. If a test of the overall model turns out to be significant, it means that each one of the betacoefficients is different from zero.
Ans: False
Response: See section 13.2 Significance Tests of the Regression Model and Its Coefficients
Difficulty: Medium
5. The F-value used for testing the significance of the overall model is computed as the ratio of
the mean square error regression (MSreg) to the sum of squares error (MSerr).
Ans: True
Response: See section 13.2 Significance Tests of the Regression Model and Its Coefficients
Difficulty: Medium
6. If a multiple regression model with two independent variables is fitted to a sample data
containing 23 sets of observations, the degrees of freedom for residual error will be 22.
Ans: False
Response: See section 13.2 Significance Tests of the Regression Model and Its Coefficients
Difficulty: Medium
7. The R2-value is calculated by dividing the sum of squares error (SSE) by the sum of squares
total (SSyy).
Ans: False
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
8. The R2-value of a multiple regression model decreases if some independent variables which
are not significantly related to the dependent variable are added to the model.
Ans: False
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
9. The numerical value of the adjusted R2 can never be greater than that of R2.
Ans: True
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Hard
10. The standard error of the estimate is computed by dividing SSE by the degrees of freedom of
error and then taking the square root.
Ans: True
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
Multiple Choice
11. The following is a partial computer output of a multiple regression analysis of a data set
containing ten sets of observations on the dependent variable, SALES (= sales volume in
thousands of dollars), and two independent variables, ADVT (= advertising expenditure in
thousands of dollars) and REPS (= number of sales representatives).
Predictor
Constant
ADVT
REPS
Coef
7.017
8.623
0.086
SE Coef
5.316
2.396
0.184
Analysis of Variance
Source
Regression
Residual Error
Total
DF
2
7
9
SS
321.11
63.39
384.50
MS
160.55
9.05
What is the predicted increase in the sales if the advertisement expenditure is increased by $2000
holding the number of sales representatives constant?
a) $8.26
b) $8623
c) $17.25
d) $17, 246
e) $1,724,600
Ans: d
Response: See section 13.1 The Multiple Regression Model
Difficulty: Hard
12. The following is a partial computer output of a multiple regression analysis of a data set
containing ten sets of observations on the dependent variable, SALES (= sales volume in
thousands of dollars), and two independent variables, ADVT (= advertising expenditure in
thousands of dollars) and REPS (= number of sales representatives).
Predictor
Constant
Coef
7.017
SE Coef
5.316
ADVT
REPS
8.623
0.086
2.396
0.184
Analysis of Variance
Source
Regression
Residual Error
Total
DF
2
7
9
SS
321.11
63.39
384.50
MS
160.55
9.05
What is the predicted value of sales if the advertisement expenditure is $3000 and there are 40
sales representatives?
a) $36.33
b) $36,326
c) $363,260
d) $3,632,600
e) $1,724,600
Ans: b
Response: See section 13.1 The Multiple Regression Model
Difficulty: Hard
13. The following is a partial computer output of a multiple regression analysis of a data set
containing ten sets of observations on the dependent variable, SALES (= sales volume in
thousands of dollars), and two independent variables, ADVT (= advertising expenditure in
thousands of dollars) and REPS (= number of sales representatives).
Predictor
Constant
ADVT
REPS
Coef
7.017
8.623
0.086
SE Coef
5.316
2.396
0.184
Analysis of Variance
Source
Regression
Residual Error
Total
DF
2
7
9
What is the numerical value of R2?
a) 83.51%
b) 78.79%
c) 77.72%
d) 98.75%
e) 100.00%
SS
321.11
63.39
384.50
MS
160.55
9.05
Ans: a
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Hard
14. The following is a partial computer output of a multiple regression analysis of a data set
containing ten sets of observations on the dependent variable, SALES (= sales volume in
thousands of dollars), and two independent variables, ADVT (= advertising expenditure in
thousands of dollars) and REPS (= number of sales representatives).
Predictor
Constant
ADVT
REPS
Coef
7.017
8.623
0.086
SE Coef
5.316
2.396
0.184
Analysis of Variance
Source
Regression
Residual Error
Total
DF
2
7
9
SS
321.11
63.39
384.50
MS
160.55
9.05
What is the standard error of the estimate?
a) 8.26
b) 6.23
c) 3.00
d) 1.72
e) 0.24
Ans: c
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Hard
15. The following is a partial computer output of a multiple regression analysis of a data set
containing ten sets of observations on the dependent variable, SALES (= sales volume in
thousands of dollars), and two independent variables, ADVT (= advertising expenditure in
thousands of dollars) and REPS (= number of sales representatives).
Predictor
Constant
ADVT
REPS
Coef
7.017
8.623
0.086
SE Coef
5.316
2.396
0.184
Analysis of Variance
Source
Regression
Residual Error
Total
DF
2
7
9
SS
321.11
63.39
384.50
MS
160.55
9.05
What is the observed F-value in the test of the significance of the overall model?
a) 8.26
b) 6.23
c) 27.05
d) 24.06
e) 17.73
Ans: e
Response: See section 13.2 Significance Tests of the Regression Model and Its Coefficients
Difficulty: Hard
16. The following is a partial computer output of a multiple regression analysis of a data set
containing ten sets of observations on the dependent variable, SALES (= sales volume in
thousands of dollars), and two independent variables, ADVT (= advertising expenditure in
thousands of dollars) and REPS (= number of sales representatives).
Predictor
Constant
ADVT
REPS
Coef
7.017
8.623
0.086
SE Coef
5.316
2.396
0.184
Analysis of Variance
Source
Regression
Residual Error
Total
DF
2
7
9
SS
321.11
63.39
384.50
MS
160.55
9.05
What is the critical or table F-value in the test of the overall model at a 0.01 level of
significance?
a) 8.26
b) 8.02
c) 7.05
d) 9.55
e) 17.73
Ans: d
Response: See section 13.2 Significance Tests of the Regression Model and Its Coefficients
Difficulty: Hard
17. A measure of goodness of fit for a multiple regression model is _____________.
a) mean square due to error
b) mean square due to regression
c) coefficient of multiple determination
d) t-statistic
e) total sum of squares
Ans: c
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
18. The range for the coefficient of multiple determination is _______________.
a) – infinity to + infinity
b) – infinity to 0
c) 0 to + infinity
d) 0 to +1
e) –1 to +1
Ans: d
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
19. The adjusted R2 accounts for ___________________________________.
a) the number of independent variables in the model
b) the number of dependent variables in the model
c) the number of observations
d) the number of the outliers in the data set
e) the number of total degrees of freedom
Ans: a
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium
20. As n, the number of observations in the data set increases the gap between R2 and adjusted
R2 ____________________________.
a) increases
b) remains the same
c) gets multiplied by n
d) gets divided by n
e) decreases
Ans: e
Response: See section 13.3 Residuals, Standard Error of the Estimate, and R2
Difficulty: Medium