Exam 15: Multiple Regression

The following regression model has been proposed to predict sales at a furniture store. a.Fully interpret the meaning of the coefficient of X₃. b.Predict sales (in dollars) for a store with competitor's previous day's sale of $3,000, a population of 10,000 within 1 mile, and six radio advertisements.

In order to test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

Exhibit 15-4 a. b. c. d. -Which equation describes the multiple regression equation?

In order to test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

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). a.Write the estimated regression equation for the relationship between the variables. b.Compute the coefficient of determination and fully interpret its meaning. c.Carry out a test of whether Y is significantly related to the independent variables. Use a 0.05 level of significance. d.Carry out a test to determine if there is a significant relationship between X₁ and Y. Use a .05 level of significance. e.How many supermarkets were in the sample used here?

In a multiple regression model, the values of the error term , $\varepsilon$ , are assumed to be

In a multiple regression model, the error term $\varepsilon$ is assumed to be a random variable with a mean of

The ratio of MSE/MSR yields

In a multiple regression analysis involving 12 independent variables and 166 observations, SSR = 878 and SSE = 122. The coefficient of determination 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). 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

A sample of 25 families was taken. The objective of the study was to estimate the factors that determine the monthly expenditure on food for families. The independent variables included in the analysis were the number of members in the family (X₁), the number of meals eaten outside the home (X₂), and a dummy variable (X₃) that equals 1 if a family member is on a diet and equals 0 if there is no family member on a diet. The following results were obtained. Analysis of Variance a. Write out the estimated regression equation. b. Interpret all coefficients. c. Test for the significance of ?1, ?2, and ?3 at the 1% level of significance.d. What are the degrees of freedom for the sum of squares explained by the regression (SSR) and the sum of squares due to error (SSE)? e. Test whether of not there is a significant relationship between the monthly expenditure on food and the independent variables. Use a .01 level of significance. Be sure to state the null and alternative hypotheses. f. Compute the coefficient of determination and explain its meaning. g. Estimate the monthly expenditure on food for a family that has 4 members, eats out 3 times, and does not have any member of the family on a diet. b.Interpret all coefficients. c.Test for the significance of $\beta$ ₁, $\beta$ ₂, and $\beta$ ₃ at the 1% level of significance. d.What are the degrees of freedom for the sum of squares explained by the regression (SSR) and the sum of squares due to error (SSE)? e.Test whether of not there is a significant relationship between the monthly expenditure on food and the independent variables. Use a .01 level of significance. Be sure to state the null and alternative hypotheses.

Exhibit 15-2 A regression model between sales (Y in $1,000), unit price (X₁ in dollars) and television advertisement (X₂ in dollars) resulted in the following function: For this model SSR = 3500, SSE = 1500, and the sample size is 18. -Refer to Exhibit 15-2. The multiple coefficient of correlation for this problem 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). Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 15-8. The estimated income of a 30-year-old male is

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: 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 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. The estimated regression equation is

The adjusted multiple coefficient of determination is adjusted for

A regression model involved 18 independent variables and 200 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

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

Below you are given a partial computer output relating the price of a company's stock (Y in dollars), the Dow Jones industrial average (X₁), and the stock price of the company's major competitor (X₂ in dollars). a.What has been the sample size for this regression analysis? b.At $\alpha$ = 0.05 level of significance, test to determine if the model is significant. That is, determine if there exists a significant relationship between the independent variables and the dependent variable. c.Determine the multiple coefficient of determination.

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The coefficient of determination for the above model is approximately