Exam 15: Multiple Regression

Exhibit 15-1 In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18x₁ +43x₂ + 87x₃ For this model SSR = 600 and SSE = 400. -Refer to Exhibit 15-1. The computed F statistics for testing the significance of the above model is

A company has recorded data on the weekly sales for its product (y), the unit price of the competitor's product (x₁), and advertising expenditures (x₂). The data resulting from a random sample of 7 weeks follows. Use Excel's Regression Tool to answer the following questions. a.What is the estimated regression equation? b.Determine whether the model is significant overall. Use $\alpha$ = 0.10. c.Determine if price is significantly related to sales. Use $\alpha$ = 0.10. d.Determine if advertising is significantly related to sales. Use $\alpha$ = 0.10. e.Find and interpret the multiple coefficient of determination.

Exhibit 15-7 A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.SSR = 165 SSE = 60 -Refer to Exhibit 15-7. If we want to test for the significance of the model at 95% confidence, the critical F value (from the table) is

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (x₁) and their gender (x₂) (0 if male and 1 if female). = 30 + 0.7x₁ + 3x₂ Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 15-8. The yearly income of a 24-year-old male individual is

The following results were obtained from a multiple regression analysis. a.How many independent variables were involved in this model? b.How many observations were involved? c.Determine the F statistic.

The following is part of the results of a regression analysis involving sales (y in millions of dollars), advertising expenditures (x₁ in thousands of dollars), and number of salespeople (x₂) for a corporation. The regression was performed on a sample of 10 observations. a.Write the regression equation. b.Interpret the coefficients of the estimated regression equation found in Part (a). c.At $\alpha$ =0.05, test for the significance of the coefficient of advertising. d.At $\alpha$ =0.05, test for the significance of the coefficient of number of salespeople. e.If the company uses $50,000 in advertisement and has 800 salespersons, what are the expected sales? Give your answer in dollars.

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄ For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The computed F statistic for testing the significance of the above model is

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (x₁) and their gender (x₂) (0 if male and 1 if female). = 30 + 0.7x₁ + 3x₂ Also provided are SST = 1,200 and SSE = 384. -In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42. The coefficient of determination is

The following results were obtained from a multiple regression analysis of supermarket profitability. The dependent variable, y, is the profit (in thousands of dollars) and the independent variables, x₁ and x₂, are the food sales and nonfood sales (also in thousands of dollars). Coefficient of determination = 0.7139 a.Write the estimated regression equation for the relationship between the variables. b.What can you say about the strength of this relationship? c.Carry out a test of whether y is significantly related to the independent variables. Use a .01 level of significance. d.Carry out a test of whether x₁ and y are significantly related. Use a .05 level of significance. e.How many supermarkets are in the sample used here?