A large auto dealership is interested in determining the number of cars that wil
ID: 3173432 • Letter: A
Question
A large auto dealership is interested in determining the number of cars that will be sold in a given quarter. The management of the dealership believes that a relationship can be found between the number of cars sold (Y), the advertised price (X1) and the current interest rates (X2). Their past experience shows that they tend to have better luck using a non-linear relationship.
NOTE: Below is the output from a regression analysis using the natural logarithm of the explanatory variables (but not of the dependent variable) in the model.
Summary measures
Multiple R
0.9326
R-Square
0.8698
Adj R-Square
0.8498
StErr of Estimate
0.0259
ANOVA Table
Source
df
SS
MS
F
p-value
Explained
2
0.0581
0.0290
43.4187
0.0000
Unexplained
13
0.0087
0.0007
Regression coefficients
Coefficient
Std Err
t-value
p-value
Constant
4.3965
0.7549
5.8239
0.0001
Log Price
-0.8255
0.2467
3.3456
0.0053
Log Interest
-0.1225
0.1880
-0.6512
0.5262
NOTE: Above is the output from a regression analysis using the natural logarithm of the explanatory variables (but not of the dependent variable) in the model.
Which of the following interpretations of the regression coefficients is correct?
If the listed price increases by $1, sales decrease by 0.8255 cars.
If the interest rate increases by 1%, sales decrease by 0.001225, given that prices remain constant.
If the interest rate increases by 1% while holding price constant, sales decrease by 12.25%.
If price increases by $1, sales decrease by 0.8255%, assuming that interest rates remain constant.
Please provide the right answer with an explanation.
Summary measures
Multiple R
0.9326
R-Square
0.8698
Adj R-Square
0.8498
StErr of Estimate
0.0259
ANOVA Table
Source
df
SS
MS
F
p-value
Explained
2
0.0581
0.0290
43.4187
0.0000
Unexplained
13
0.0087
0.0007
Regression coefficients
Coefficient
Std Err
t-value
p-value
Constant
4.3965
0.7549
5.8239
0.0001
Log Price
-0.8255
0.2467
3.3456
0.0053
Log Interest
-0.1225
0.1880
-0.6512
0.5262
Explanation / Answer
Explanation: If the interest rate increases by 1% while holding the price constant, sales decrease by 12.25%. The main interpretation of coefficients is based on the other independent variable should hold it as a constant and the amount of increase or decrease based on the sign of the coefficient can be interpretted.
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