Response to the following MCQ's:
1. The y-intercept (b0) represents the
a. predicted value of Y when X = 0.
b. change in estimated average Y per unit change in X.
c. predicted value of Y.
d. variation around the sample regression line.
2. The least squares method minimizes which of the following?
a. SSR
b. SSE
c. SST
d. All of the above
TABLE 1
A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:
City Price ($) Sales
River Falls 1.30 100
Hudson 1.60 90
Ellsworth 1.80 90
Prescott 2.00 40
Rock Elm 2.40 38
Stillwater 2.90 32
Referring to Table 1, what is the estimated slope parameter for the candy bar price and sales data?
a. 161.386
b. 0.784
c. -3.810
d. -48.193
4. Referring to Table 1, what is the percentage of the total variation in candy bar sales explained by the regression model?
a. 100%
b. 88.54%
c. 78.39%
d. 48.19%
5. Referring to Table 1, what is the standard error of the estimate, SYX, for the data?
a. 0.784
b. 0.885
c. 12.650
d. 16.299
6. Referring to Table 1, if the price of the candy bar is set at $2, the predicted sales will be
a. 30
b. 65
c. 90
d. 100
7. If the Durbin-Watson statistic has a value close to 0, which assumption is violated?
a. Normality of the errors.
b. Independence of errors.
c. Homoscedasticity.
d. None of the above.
8. If the Durbin-Watson statistic has a value close to 4, which assumption is violated?
a. Normality of the errors.
b. Independence of errors.
c. Homoscedasticity.
d. None of the above.
9. If the correlation coefficient (r) = 1.00, then
a. the y-intercept (b0) must equal 0.
b. the explained variation equals the unexplained variation.
c. there is no unexplained variation.
d. there is no explained variation.
10. In a simple linear regression problem, r and b1
a. may have opposite signs.
b. must have the same sign.
c. must have opposite signs.
d. are equal.
11. The strength of the linear relationship between two numerical variables may be measured by the
a. scatter diagram.
b. y-intercept.
c. slope.
d. coefficient of correlation.
12. The width of the prediction interval estimate for the predicted value of Y is dependent on
a. the standard error of the estimate.
b. the value of X for which the prediction is being made.
c. the sample size.
d. All of the above.
TABLE 2
The following Excel tables are obtained when "Score received on an exam (measured in percentage points)" (Y) is regressed on "percentage attendance" (X) for 22 students in a Statistics for Business and Economics course.
Regression Statistics
Multiple R 0.142620229
R Square 0.02034053
Adjusted R Square -0.028642444
Standard Error 20.25979924
Observations 22
Coefficients Standard Error t Stat p-value
Intercept 39.39027309 37.24347659 1.057642216 0.302826622
Attendance 0.340583573 0.52852452 0.644404489 0.526635689
13. Referring to Table 2, which of the following statements is true?
a. -2.86% of the total variability in score received can be explained by percentage attendance.
b. -2.86% of the total variability in percentage attendance can be explained by score received.
c. 2% of the total variability in score received can be explained by percentage attendance.
d. 2% of the total variability in percentage attendance can be explained by score received.
14. In a multiple regression problem involving two independent variables, if b1 is computed to be +2.0, it means that
a. the relationship between X1 and Y is significant.
b. the estimated average of Y increases by 2 units for each increase of 1 unit of X1, holding X2 constant.
c. the estimated average of Y increases by 2 units for each increase of 1 unit of X1, without regard to X2.
d. the estimated average of Y is 2 when X1 equals zero.
15. In a multiple regression model, which of the following is correct regarding the value of the adjusted r2?
a. It can be negative.
b. It has to be positive.
c. It has to be larger than the coefficient of multiple determination.
d. It can be larger than 1.
16. A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee
has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of 8 employees provides the
following:
TABLE 3
Employee Y X1 X2
1 100 10 7
2 90 3 10
3 80 8 9
4 70 5 4
5 60 5 8
6 50 7 5
7 40 1 4
8 30 1 1
Referring to Table 3, for these data, what is the value for the regression constant, b0?
a. 0.998
b. 3.103
c. 4.698
d. 21.293
17. Referring to Table 3, if an employee who had been with the company 5 years scored a 9 on the aptitude test, what would his estimated expected sales be?
a. 79.09
b. 60.88
c. 55.62
d. 17.98
TABLE 4
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.991
R Square 0.982
Adjusted R Square 0.976
Standard Error 0.299
Observations 10
ANOVA
Df SS MS F Signif F
Regression 2 33.4163 16.7082 186.325 0.0001
Residual 7 0.6277 0.0897
Total 9 34.0440
Coeff StdError t Stat P-value
Intercept -0.0861 0.5674 -0.152 0.8837
GDP 0.7654 0.0574 13.340 0.0001
Price -0.0006 0.0028 -0.219 0.8330
18. Referring to Table 4, when the economist used a simple linear regression model with consumption as the dependent variable and GDP as the independent variable, he obtained an r2 value of 0.971. What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression?
a. 98.2
b. 11.1
c. 2.8
d. 1.1
19. Referring to Table 4, what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index
of 150?
a. $1.39 billion
b. $2.89 billion
c. $4.75 billion
d. $9.45 billion
20. Referring to Table 4, to test for the significance of the coefficient on aggregate price index, the value of the relevant t-statistic is
a. 2.365
b. 0.143
c. -0.219
d. -1.960
21. Referring to Table 4, to test whether gross domestic product has a positive impact on consumption, the p-value is
a. 0.00005
b. 0.0001
c. 0.9999
d. 0.99995