Exam 13: Multiple Regression

Exhibit 13-4 a. Y=β₀ + β₁X1 + β2X2 + ε b. EY)=β₀ + β₁X1 + β2X2 + ε c. $\hat { Y }$ =b₀ + b₁X1 + b2X2 d. EY)=β₀ + β₁X1 + β2X2 -Refer to Exhibit 13-4. Which equation describes the multiple regression equation?

Exhibit 13-2 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: $\hat { Y }$ =7-3X1+5X2 For this model SSR = 3500, SSE = 1500, and the sample size is 18. -Refer to Exhibit 13-2. The coefficient of X2 indicates that if television advertising is increased by $1 holding the unit price constant), sales are expected to

Exhibit 13-12 In a laboratory experiment, data were gathered on the life span Y in months) of 33 rats, units of daily protein intake X1), and whether or not agent X2 a proposed life extending agent) was added to the rats diet X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed. $\hat { Y }$ =36+0.8X1 - 1.7X2 Also provided are SSR = 60 and SST = 180. -Refer to Exhibit 13-12. From the above function, it can be said that the life expectancy of rats that were given agent X2 is

Exhibit 13-8 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). $\hat { Y }$ =30+0.7X1+3X2 Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 13-8. The estimated income of a 30-year-old male is

A regression was performed on a sample of 16 observations. The estimated equation is =23.5 - 14.28X1+6.72X2+15.68X3. The standard errors for the coefficients are Sb₁ = 4.2, Sb2 = 5.6, and Sb3 = 2.8. For this model, SST = 3809.6 and SSR = 3285.4. $\hat { Y }$ a. Compute the appropriate t ratios. b. Test for the significance of β₁, β2 and β3at the 5% level of significance. c. Do you think that any of the variables should be dropped from the model? Explain. d. Compute R² and Ra2 . Interpret R². e. Test the significance of the relationship among the variables at the 5% level of significance.

In a multiple regression model, the error term ε is assumed to

Exhibit 13-11 Below you are given a partial computer output based on a sample of 25 observations. Coefficient Standard Error Constant 145 29 20 5 -18 6 4 4 -Refer to Exhibit 13-11. The estimated regression equation is

A regression model relating units sold Y), price X1), and whether or not promotion was used X2 = 1 if promotion was used and 0 if it was not) resulted in the following model. $\hat { Y }$ =120 - 0.03X1 =0.7X2 and the following information is provided. n= 15 Sb₁ = .01 Sb2 = 0.1 a. Is price a significant variable? b. Is promotion significant?

Exhibit 13-9 In a regression analysis involving 25 observations, the following estimated regression equation was developed. $\hat { Y }$ =10 - 18X1+3X2+14X3 Also, the following standard errors and the sum of squares were obtained. Sb₁ = 3 Sb2 = 6 Sb3 = 7 SST = 4,800 SSE = 1,296 -Refer to Exhibit 13-9. The coefficient of X2

Exhibit 13-8 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). $\hat { Y }$ =30+0.7X1+3X2 Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 13-8. The test statistic for testing the significance of the model is

Exhibit 13-8 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). $\hat { Y }$ =30+0.7X1+3X2 Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 13-8. If we want to test for the significance of the model, the critical value of F at 95% confidence is

Exhibit 13-10 In a regression model involving 30 observations, the following estimated regression equation was obtained. $\hat { Y }$ =170+34X1 - 3X2+8X3+58X4+3X5 For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 13-10. The value of MSE is

In multiple regression analysis, the word linear in the term "general linear model" refers to the fact that

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

Multiple regression analysis was used to study how an individual's income Y in thousands of dollars) is influenced by age X1 in years), level of education X2 ranging from 1 to 5), and the person's gender X3 where 0 =female and 1=male). The following is a partial result of a computer program that was used on a sample of 20 individuals. Coefficient Standard Error X1 0.6251 0.094 X2 0.9210 0.190 X3 -0.5100 0.920 Analysis of Variance Source of Variation Degrees of Freedom Sum of Squares Mean Square F Regression 84 Error 112 a. Compute the coefficient of determination. b. Perform a t test and determine whether or not the coefficient of the variable "level of education" i.e., X2) is significantly different from zero. Let α = 0.05. c. At α = 0.05, perform an F test and determine whether or not the regression model is significant. d. As you note the coefficient of X3 is -0.510. Fully interpret the meaning of this coefficient.

A model in the form of y = β₀ + β₁z1 + β2z2 + . . . +βpzp + ε where each independent variable zj for j = 1, 2, . . ., p) is a function of xj . xj is known as the

Exhibit 13-10 In a regression model involving 30 observations, the following estimated regression equation was obtained. $\hat { Y }$ =170+34X1 - 3X2+8X3+58X4+3X5 For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 13-10. The degrees of freedom associated with SSE are

Exhibit 13-2 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: $\hat { Y }$ =7-3X1+5X2 For this model SSR = 3500, SSE = 1500, and the sample size is 18. -Refer to Exhibit 13-2. The multiple coefficient of correlation for this problem is

The following are partial 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. Coeffcient Standard Error Constant 50.00 20.00 3.60 1.20 0.20 0.20 a. At α = 0.05, test for the significance of the coefficient of advertising. b. If the company uses $20,000 in advertisement and has 300 salespersons, what are the expected sales? Give your answer in dollars.)

Exhibit 13-7 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 13-7. If we want to test for the significance of the model at 95% confidence, the critical F value from the table) is