Exam 16: Regression Analysis: Model Building

A test 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. = 10 - 18x₁ + 3x₂ + 14x₃ 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 model

The parameters of nonlinear models have exponents

Exhibit 16-1 In a regression analysis involving 25 observations, the following estimated regression equation was developed. = 10 - 18x₁ + 3x₂ + 14x₃ 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. If you want to determine whether or not the coefficients of the independent variables are significant, the critical value of t statistic at $\alpha$ = 0.05 is

Consider the following data. Use Excel's Regression Tool to estimate a general linear model that uses a reciprocal transformation on the dependent variable.

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 = 0.60 SSR = 4,800 Total number of observations n = 35 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.

A regression model relating a dependent variable, y, with one independent variable, x₁, resulted in an SSE of 400. Another regression model with the same dependent variable, y, and two independent variables, x₁ and x₂, resulted in an SSE of 320. At $\alpha$ = .05, determine if x₂ contributed significantly to the model. The sample size for both models was 20.

Exhibit 16-3 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 16-3. We want to test whether the parameter $\beta$ ₂ is significant. The test statistic equals

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. = 36 + 0.8x₁ - 1.7x₂ Also provided are SSR = 60 and SST = 180. -Refer to Exhibit 16-4. The degrees of freedom associated with SSR are

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. = 36 + 0.8x₁ - 1.7x₂ Also provided are SSR = 60 and SST = 180. -Refer to Exhibit 16-4. The life expectancy of a rat that was given 3 units of protein daily, and who took agent x₂ is

When autocorrelation is present, one of the assumptions of the regression model is violated and that assumption is:

The null hypothesis in the Durbin-Watson test is always that there is

A regression analysis was applied in order to determine the relationship between a dependent variable and 14 independent variables. The following information was obtained from the regression analysis.R Square = 0.70 SSR = 7,000 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.

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. = 36 + 0.8x₁ - 1.7x₂ Also provided are SSR = 60 and SST = 180. -Refer to Exhibit 16-4. The degrees of freedom associated with SSE are

Consider the following data. Use Excel's Regression Tool to estimate a general linear model that uses a reciprocal transformation on the dependent variable.

Thirty four observations of a dependent variable (y), and two independent variables resulted in an SSE of 300. When a third independent variable was added to the model, the SSE was reduced to 250. At a 5% level of significance, determine if the third independent variable contributes significantly to the model.

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. = 36 + 0.8x₁ - 1.7x₂ 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

We want to test whether or not the addition of 3 variables to a model will be statistically significant. You are given the following information based on a sample of 25 observations. = 62.42 - 1.836x₁ + 25.62x₂ SSE = 725 SSR = 526 The equation was also estimated including the 3 variables. The results are = 59.23 - 1.762x₁ + 25.638x₂ + 16.237x₃ + 15.297x₄ - 18.723x₅ SSE = 520 SSR = 731 a.State the null and alternative hypotheses. b.Test the null hypothesis at the 5% level of significance.

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 16-2 In a regression model involving 30 observations, the following estimated regression equation was obtained. = 170 + 34x₁ - 3x₂ + 8x₃ + 58x₄ + 3x₅ For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 16-2. The degrees of freedom associated with SSR are