Question

QUESTION 16 13)-19) A company analyst is interested in the relationship between number of cars sold per month (in 1,000s) and three independent variables: price per gallon of gasoline (X1=Gas, in $), the prevailing interest rate for car loans (X2=Interest, in %), and the car model (X3=model, with X3=1, if the car is standard; and X3=0, if the car is luxury). He took a sample of 50 observations and obtained the following output: Coefficients Standard Errort Stat P-value Intercept 96.0744 10.0080 5.60 0.0001 GAS-16.1436 9.3158 -1.73 0.0927 INTEREST -2.3322 0.3624 -6.43 0.0001 MODEL 14.4222 1.5869 9.09 0.0001 Which of the following best represents the interpretation of the slope b1? For each one-dollar increases in the gas price, the number of cars sold (in 1,000s) will decrease by 16.1436 on average, if INTEREST and MODEL are held constant. For each one-dollar increases in the gas price, the number of cars sold (in 1,000s) will decrease by -16.1436 on average. For each one-dollar increases in the gas price, the number of cars sold (in 1,000s) will decrease by 16.1436 on average. For each one-dollar increases in the gas price, the number of cars sold (in 1,000s) will decrease by -16.1436 on average, if INTEREST and MODEL are held constant. QUESTION 17 13)-19) A company analyst is interested in the relationship between number of cars sold per month (in 1,000s)) and three independent variables: price per gallon of gasoline (X1=Gas, in $), the prevailing interest rate for car loans (X2=Interest, in %), and the car model (X3=model, with X3=1, if the car is standard; and X3=0, if the car is luxury). He took a sample of 50 observations and obtained the following output: Coefficients Standard Errort Stat P-value Intercept 96.0744 10.0080 5.60 0.0001 GAS -16.1436 9.3158 -1.73 0.0927 INTEREST -2.3322 0.3624 -6.43 0.0001 MODEL 14.4222 1.5869 9.09 0.0001 At the 0.01 level of significance, what conclusion should we draw regarding the inclusion of INTEREST in the regression model? The INTEREST variable is not sign cant in explaining the sales and should be included in the model because its p value is more than 0.01. The INTEREST variable is not significant in explaining the sales and should be included in the model because its p value is less than 0.01. The INTEREST variable is significant in explaining the sales and should be included in the model because its p value is more than 0.01. The INTEREST variable is significant in explaining the sales and should be included in the model because its p value is less than 0.01.

Answer 1

16)

The value of b₁ is -16.1436.

This means that for each 1-dollar increase in the gas price, the number of cars sold (in 1000s) will decrease by 16.1436 on an average, if the other variables INTEREST and MODEL are held constant.

Hence 1st option.

17)

Since the p-value for the coefficient of INTEREST variable is 0.0001 which is less than 0.01, thus we can reject the null hypothesis and conclude that the INTEREST variable is significant in explaining the sales and should be included in the model because its p-value is less than 0.01.

Hence 4th option.