1. You give a pre-employment examination to your applicants. The test is scored from 1 to 100. You have data on their sales at the end of one year measured in dollars. You want to know if there is any linear relationship between pre-employment examination score and sales. An appropriate test to use is the t test on the population correlation coefficient.
A) True
B) False
2. Testing for the existence of correlation is equivalent to
A) testing for the existence of the slope (β1).
B) testing for the existence of the intercept (β0).
C) the confidence interval estimate for predicting Y.
D) None of the above.
3. Suppose you were given data on the price of a gallon of ice cream and the sales of ice cream (in gallons) for 60 days. The correlation between ads and sales is -0.40. Does this indicate a significant negative relationship between price and sales at the 0.005 level of significance?
A) Yes
B) No
C) Not enough information to determine significance
4. If one examines the relationship between two variables, the correlation (r) and the slope coefficient (b1) in a simple regression model
A) may have opposite signs.
B) must have the same signs.
C) must have opposite signs.
D) are equal.
5. If one examines the relationship between two variables, the correlation (r) and the slope coefficient (b1) in a multiple regression model
A) may have opposite signs.
B) must have the same signs.
C) must have opposite signs.
D) are equal.
6. A quality control expert was investigating the relationship between training (in hours) and worker efficiency (number of product errors made per day). His results indicated a correlation coefficient of zero. Which of the following is NOT a reason for this result?
A) Training is not effective at changing worker efficiency.
B) Correlation can only capture positive relationships between variables not the negative relationship apparent in the use of these variables.
C) The relationship between training and worker efficiency is non-linear.
D) A third variable not included in the analysis may be affecting both hours of training and worker efficiency.
7. In a regression model with one independent variable X, the intercept or constant (b0) represents the
A) predicted value of the dependent variable Y when the X = 0.
B) estimated average per unit change in the dependent variable for every unit change in X.
C) predicted or fitted value of dependent variable.
D) average variation around the sample regression line.
8. In a regression model with one independent variable X, the slope coefficient (b1) represents the
A) predicted value of the dependent variable Y when the X = 0.
B) estimated average per unit change in the dependent variable for every unit change in X.
C) predicted or fitted value of dependent variable.
D) average variation around the sample regression line.
9. R2, the coefficient of determination, detects the strength of the relationship between the dependent variable and all independent variables.
A) True
B) False
10. When an explanatory or independent variable is added to a multiple regression model, R2 will always increase.
A) True
B) False
11. If one tests to see if the value of R2 is statistically different from zero, one should use a
A) t-statistic.
B) F-statistic.
C) z-statistic.
D) correlation coefficient (r).
Situation 7.2.1:
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. The output is provided below:
|
Variable
|
Coefficient
|
t-statistic
|
|
Constant
|
-1.633
|
-0.281
|
|
Income
|
0.448
|
3.954
|
|
Size
|
4.216
|
5.286
|
|
School
|
-0.6517
|
-1.509
|
|
R2 =0.75; Adjusted R2 = 0.73
|
|
F = 6.43
|
12. Referring to Situation 7.2.1, which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?
A) 0.01
B) 0.025
C) 0.05
D) 0.15
13. Referring to Situation 7.2.1, what are the degrees of freedom for this F-statistic?
A) 46 for the numerator, 4 for the denominator
B) 3 for the numerator, 49 for the denominator
C) 46 for the numerator, 49 for the denominator
D) 3 for the numerator, 46 for the denominator
14. Referring to Situation 7.2.1, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?
A) 0.00005
B) 0.001
C) 0.01
D) 0.05
15. Referring to Situation 7.2.1, what is the predicted house size (in hundreds of square feet) for an individual earning an annual income of $40,000, having a family size of four, and going to school a total of 13 years?
A) 11.43
B) 15.15
C) 24.68
D) 53.87
16. Referring to Situation 7.2.1, one individual in the sample had an annual income of $100,000, a family size of 10, and an education of 16 years. This individual owned a home with an area of 7,000 square feet (House = 70.00). What is the residual (in hundreds of square feet) for this data point?
A) 7.40
B) 2.52
C) - 2.52
D) - 4.89
Situation 7.2.2:
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The output below shows results
|
Variable
|
Coefficient
|
Standard Error
|
|
Constant
|
15,800
|
6038.30
|
|
Capital
|
0.124
|
0.204
|
|
Wage
|
7.7076
|
1.473
|
|
R2 =0.69; Adjusted R2 = 0.66
|
|
F = 25.43
|
17. Referring to Situation 7.2.2, which of the independent variables (capital, wages) in the model are significant at the 5% level? (Hint: the table reports standard errors not t-statistics)
A) Capital, Wages
B) Capital
C) Wages
D) None of the above
18. Referring to Situation 7.2.2, the observed value of the F-statistic is given on the printout as 25.43. What are the degrees of freedom for this F-statistic?
A) 25 for the numerator, 2 for the denominator
B) 2 for the numerator, 23 for the denominator
C) 23 for the numerator, 25 for the denominator
D) 2 for the numerator, 25 for the denominator
19. The economist in Situation 7.2.2 decided to add a new variable, energy expenditures, to the model. The new results included an R2 = 0.78 and Adjusted R2 = 0.72. How do you interpret these changes?
A) Since R2 increased, the new variable was an important addition to the model.
B) Since Adjusted R2 increased, the new variable was an important addition to the model.
C) One cannot evaluate the importance of the new variable to the model without knowing either the standard error or t-statistic for the variable's coefficient.
20. There are several reasons why choices between alternative regression models should NOT be based on which model has the highest R2. Which of the following is NOT one of those reasons?
A) Models using time series data will have higher R2 than models using cross-sectional data.
B) Some variables are inherently more unstable and thus harder to predict.
C) R2 indicates relationships not causality.
D) R2 captures the individual effects of variables but not the effects of all variables.