EF 507PS-Chapter 12FALL 2008
QUESTIONS 1 THROUGH 3 ARE BASED ON THE FOLLOWING INFORMATION:
The manager of a used-car dealership is very interested in the resale price of used cars. The manager feels that the age of the car is important in determining the resale value. He collects data on the age and resale value of 15 cars and runs a regression analysis with the value of the car (in thousands of dollars) as the dependent variable and the age of the car (in years) as the independent variable. Unfortunately, he spilled his coffee on the printout and lost some of the results, identified by “A” through “F”. The partial results left are displayed below.
SUMMARY OUTPUTObservations / 15
Coefficients / Standard Error / t Stat / P-value
Intercept / “A” / 3.835 / 5.988 / 0.000
Age / “B” / 0.640 / -1.776 / “G”
1.What is the value of *A*?
A)9.35
B)3.06
C)9.82
D)22.96
2.What is the value of *B*?
A)1.136
B)-1.136
C)0.278
D)-0.278
3.What is the approximate value of *G*?
A)0.025
B)0.05
C)0.10
D)0.01
QUESTIONS 4 THROUGH 5 ARE BASED ON THE FOLLOWING INFORMATION:
An insurance company analyst is interested in analyzing the dollar value of damage in automobile accidents. She collects data from 115 accidents, and records the amount of damage as well as the age of the driver. The results of her regression analysis are listed below.
SUMMARY OUTPUTRegression Statistics
Observations / 115
Coefficients / Standard Error / t Stat / P-value
Intercept / 10725.802 / 1535.215 / 6.987 / 0.000
Age / 69.964 / 34.625 / 2.021 / 0.046
4.How would you best explain the y-intercept in this situation?
A)For each additional 1-year increase in the age of the driver, we would expect damage to increase by $10,726.
B)For each additional 1-year increase in the age of the driver, we would expect damage to increase by $70.
C)It makes no sense to explain the intercept in this situation, since we can not have a driver with age of zero.
D)The average amount of damage was $10,726.
5.On average, what would be the dollar value of an accident involving a 25-year-old driver?
A)$11,836.56
B)$10,795.47
C)$13,372.58
D)$2,474.90
6.A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: = 120 + 5x. This implies that if the height is increased by 1 inch, the weight is expected to:
A)increase by 1 pound
B)decrease by 1 pound
C)decrease by 24 pounds
D)increase by 5 pounds
7.A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: = 75 + 5x. This implies that if advertising is $800, then the predicted amount of sales (in dollars) is:
A)$4075
B)$115,000
C)$64,000
D)$79,000
QUESTIONS 8 AND 9 ARE BASED ON THE FOLLOWING INFORMATION:
In a recent survey, 250 adults were asked about their monthly expenditures (in dollars) on the lottery. In addition, data were collected about the number of years of education they had. A simple regression was run, and the following results were obtained: = 35.6, = -2.37, = 18.9, and = 1.28 .
8.How would you interpret the slope coefficient?
9.Test.
QUESTIONS 10 THROUGH 13 ARE BASED ON THE FOLLOWING INFORMATION:
You are interested in exploring the relationship between the income of professors (measured in thousands of dollars) and the number of years they have been employed by the university. You collect the following data from eight professors.
Years of Employment / 14 / 23 / 14 / 19 / 19 / 12 / 10 / 4Income / 69.7 / 71.2 / 68.2 / 71.5 / 69.7 / 70.1 / 67.6 / 66.1
Use computer to run the simple linear regression analysis of income on length of employment.
10.What is the estimated regression line?
11.What is the estimated income for a professor with 20 years of employment?
12.How would you interpret the slope coefficient?
13.Test using the t-test.
QUESTIONS 14 THROUGH 16 ARE BASED ON THE FOLLOWING INFORMATION:
Given the estimated regression equation: = 95 + 8X.
14.What is the change in Y when X changes by +2?
15.What is the change in Y when X changes by -3?
16.What is the predicted value of Y when X =10?
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