Exam 15: Multiple Regression

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.If the company uses $40,000 in advertisement and has 30 salespersons, what are the expected sales? Give your answer in dollars. b.At $\alpha$ = 0.05, test for the significance of the coefficient of advertising. c.At $\alpha$ = 0.05, test for the significance of the coefficient of the number of salespeople.

A multiple regression model has the form As X increases by 1 unit (holding W constant), Y is expected to

In regression analysis, an outlier is an observation whose

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. We want to test whether the parameter $\beta$ ₁ is significant. The test statistic equals

A multiple regression model has

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

The following regression model has been proposed to predict monthly sales at a shoe store. a.Predict sales (in dollars) for the shoe store if the competitor's previous month's sales were $9,000, the store's previous month's sales were $30,000, and no radio advertisements were run. b.Predict sales (in dollars) for the shoe store if the competitor's previous month's sales were $9,000, the store's previous month's sales were $30,000, and 10 radio advertisements were run.

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. The sum of squares due to error (SSE) equals

In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240. The coefficient of determination is

Exhibit 15-6 Below you are given a partial computer output based on a sample of 16 observations. -Refer to Exhibit 15-6. Carry out the test to determine if there is a relationship among the variables at the 5% level. The null hypothesis should

For a multiple regression model, SSR = 600 and SSE = 200. The multiple coefficient of determination is

A regression model involved 5 independent variables and 136 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

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. If we want to test for the significance of the model, the critical value of F at 95% confidence is

In regression analysis, the response variable is the

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

A regression analysis involved 6 independent variables and 27 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

Below you are given a partial computer output based on a sample of 12 observations relating the number of personal computers sold by a computer shop per month (Y), unit price (X₁ in $1,000) and the number of advertising spots (X₂) used on a local television station. a. Use the output shown above and write an equation that can be used to predict the monthly sales of computers. b. Interpret the coefficients of the estimated regression equation found in Part a.c. If the company charges $2,000 for each computer and uses 10 advertising spots, how many computers would you expect them to sell? d. At  = 0.05, test to determine if the price is a significant variable.e. At  = 0.05, test to determine if the number of advertising spots is a significant variable.

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. The coefficient of determination is

A regression model involving 3 independent variables for a sample of 20 periods resulted in the following sum of squares. a.Compute the coefficient of determination and fully explain its meaning. b.At $\alpha$ = 0.05 level of significance, test to determine whether or not there is a significant relationship between the independent variables and the dependent variable.

Exhibit 15-4 a. b. c. d. -Which equation gives the estimated regression line?