A+ Answers

The district sales manager for a major automobile manufacturer is studying car sales. Specifically, he would like to determine what factors affect the number of cars sold at a dealership. To investigate, he randomly selects 12 dealers. From these dealers he obtains the number of cars sold last month (Y), the minutes of radio advertising expenditures purchased last month (X1), and the number of full-time salespeople employed in the dealership (X2).
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.960193921
R Square 0.921972366
Adjusted R Square 0.91325455
Standard Error 7.166959066
Observations 12
ANOVA
df SS MS F Significance F
Regression 2 5462.378946 2731.189473 1.03542E-05
Residual 9  51.36530226
Total 11 5924.666667
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 25.29519619 11.5689425 2.186474364 -0.875569888 51.46596227 -0.875569888 51.46596227
X Variable 1 2.618717736 1.605661888 1.630927256 1.248615362 3.988820111 1.248615362 3.988820111
X Variable 2 5.023270121 0.900327718 5.579379618 2.986587328 7.059952913 2.986587328 7.059952913
Y = Number of Cars Sold Last Month
X1 = Minutes of Radio Advertising Expenditures Last Month
X2 = Number of Full-Time Salespeople Employed in the Dealership
(a) Express the estimated multiple regression equation in standard form.
(b) Which of the explanatory variables (if any) are statistically significant (05 alpha or one-side p level) in explaining the number of cars sold? Hint: Conduct a formal hypothesis test for each estimated regression slope coefficient (B1HAT &B2HAT).
(c) Would you recommend dropping any of the explanatory variables from the model? Please explain.
(d) Give an interpretation (as applicable to the data) for each of the estimated regression coefficients.
(e) What percent of the total variation in the number of cars sold is explained by the regression model?
(f) Would the estimated regression equation be suitable to forecast the number of cars sold? Provide a brief evaluation of the estimated regression equation in terms of the regression statistics.
(g) Forecast the number of cars sold when advertising minutes equals 20 (X1) and the number of salespeople equals 13 (X2).