Exam 16: Regression Analysis: Model Building

In a regression analysis involving 20 observations and five independent variables, the following information was obtained. Fill in all the blanks in the above ANOVA table.

We are interested in determining what type of model best describes the relationship between two variables x and y. a.For a given data set, an estimated regression equation relating x and y of the form was developed, using Excel. The results are shown below. Comment on the adequacy of this equation for predicting y. Let $\alpha$ = .05. b.An estimated regression equation for the same data set (as in part a) of the form was developed. The Excel output is shown below. Comment on the adequacy of this equation for predicting y. Let $\alpha$ = .05. c.Use the results of Part b and predict y when x = 4.

Exhibit 16-1 In a regression analysis involving 25 observations, the following estimated regression equation was developed. Also, the following standard errors and the sum of squares were obtained. S_b1 = 3 S_b2 = 6 S_b3 = 7 SST = 4,800 SSE = 1,296 -Refer to Exhibit 16-1. The coefficient of X₂

A test used to determine whether or not first order autocorrelation is present is

Exhibit 16-1 In a regression analysis involving 25 observations, the following estimated regression equation was developed. Also, the following standard errors and the sum of squares were obtained. S_b1 = 3 S_b2 = 6 S_b3 = 7 SST = 4,800 SSE = 1,296 -Refer to Exhibit 16-1. The coefficient of X₁

Exhibit 16-1 In a regression analysis involving 25 observations, the following estimated regression equation was developed. Also, the following standard errors and the sum of squares were obtained. S_b1 = 3 S_b2 = 6 S_b3 = 7 SST = 4,800 SSE = 1,296 -Refer to Exhibit 16-1. The coefficient of X₃

The following regression model is known as

Exhibit 16-4 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. Also provided are SSR = 60 and SST = 180. -Refer to Exhibit 16-4. If we want to test for the significance of the model, the critical value of F at 95% confidence is

When a regression model was developed relating sales (Y) of a company to its product's price (X₁), the SSE was determined to be 495. A second regression model relating sales (Y) to product's price (X₁) and competitor's product price (X₂) resulted in an SSE of 396. At $\alpha$ = 0.05, determine if the competitor's product's price contributed significantly to the model. The sample size for both models was 33.

Exhibit 16-1 In a regression analysis involving 25 observations, the following estimated regression equation was developed. Also, the following standard errors and the sum of squares were obtained. S_b1 = 3 S_b2 = 6 S_b3 = 7 SST = 4,800 SSE = 1,296 -Refer to Exhibit 16-1. The multiple coefficient of determination is

Exhibit 16-4 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. Also provided are SSR = 60 and SST = 180. -Refer to Exhibit 16-4. The test statistic for testing the significance of the model 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. a.At $\alpha$ = 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.)

All the variables in a multiple regression analysis

The joint effect of two variables acting together is called

Exhibit 16-4 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. Also provided are SSR = 60 and SST = 180. -Refer to Exhibit 16-4. The life expectancy of a rat that was given 2 units of agent X₂ daily, but was not given any protein is

The correlation in error terms that arises when the error terms at successive points in time are related is termed

The following estimated regression equation has been developed for the relationship between y, the dependent variable, and x, the independent variable. The sample size for this regression model was 23, and SSR = 600 and SSE = 400. a.Compute the coefficient of determination. b.Using $\alpha$ = .05, test for a significant relationship.

A regression analysis was applied in order to determine the relationship between a dependent variable and 4 independent variables. The following information was obtained from the regression analysis. R Square = 0.80 SSR = 680 Total number of observations n = 45 a.Fill in the blanks in the following ANOVA table. b.At $\alpha$ = 0.05 level of significance, test to determine if the model is significant.

In a regression analysis involving 18 observations and four independent variables, the following information was obtained. Based on the above information, fill in all the blanks in the following ANOVA table.

In a regression analysis involving 21 observations and 4 independent variables, the following information was obtained. = 0.80 S = 5.0 Based on the above information, fill in all the blanks in the following ANOVa.Hint: = , but also = 1- .