In order to determine whether or not the sales of a company (y in millions of dollars) is related to advertising expenditures (x1 in millions of dollars) and the number of salespeople (x2), data were gathered for 10 (n) years. Part of the regression results are shown below. Coefficients Standard Error Intercept 7.0174 1.8972 x1 8.6233 2.3968 x2 0.0858 0.1845 ANOVA df SS MS F Regression 321.11 Residual (Error) 63.39 A. Use the above results and write the multiple regression equation that can be used to predict sales and interpret the statical meaning of the estimated slope coefficient b1(for advertising expenditure). B. Estimate the sales volume for an advertising expenditure of 3.5 million dollars and 45 salespeople. Give your answer in dollars. Please show all the relevant calculations. C. At α = 0.05, test to determine through an F-test if the fitted equation developed in Part A represents a significant relationship between the independent variables and the dependent variable. Please show all the relevant calculations.
In order to determine whether or not the sales of a company (y in millions of dollars) is related to advertising expenditures (x1 in millions of dollars) and the number of salespeople (x2), data were gathered for 10 (n) years. Part of the regression results are shown below.
|
|
Coefficients |
Standard Error |
|
Intercept |
7.0174 |
1.8972 |
|
x1 |
8.6233 |
2.3968 |
|
x2 |
0.0858 |
0.1845 |
|
ANOVA |
|
|
|
|
|
|
df |
SS |
MS |
F |
|
Regression |
|
321.11 |
|
|
|
Residual (Error) |
|
63.39 |
|
|
|
A. Use the above results and write the multiple regression equation that can be used to predict sales and interpret the statical meaning of the estimated slope coefficient b1(for advertising expenditure). |
|
B. Estimate the sales volume for an advertising expenditure of 3.5 million dollars and 45 salespeople. Give your answer in dollars. Please show all the relevant calculations. |
|
C. At α = 0.05, test to determine through an F-test if the fitted equation developed in Part A represents a significant relationship between the independent variables and the dependent variable. Please show all the relevant calculations. |
|
D. At α = .05, test to see through a t-test if β1 is significantly different from zero. Please show all the relevant calculations. |
|
E. Determine the multiple coefficient of determination (R^2). Please show all the relevant calculations. |
|
F. Compute the adjusted coefficient of determination (Adj R^2). Please show all the relevant calculations. |
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