Exam 16: Regression Analysis: Model Building

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Exhibit 16-1 In a regression analysis involving 25 observations, the following estimated regression equation was developed. 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<sub>b1</sub> = 3 S<sub>b2</sub> = 6 S<sub>b3</sub> = 7 SST = 4,800 SSE = 1,296 -Refer to Exhibit 16-1. The test statistic for testing the significance of the model is 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 16-1. The test statistic for testing the significance of the model is

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Exhibit 16-2 In a regression model involving 30 observations, the following estimated regression equation was obtained. Exhibit 16-2 In a regression model involving 30 observations, the following estimated regression equation was obtained.   For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 16-2. The value of MSE is For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 16-2. The value of MSE is

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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. 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 (X<sub>1</sub>), and whether or not agent X<sub>2</sub> (a proposed life extending agent) was added to the rats diet (X<sub>2</sub> = 0 if agent X<sub>2</sub> was not added, and X<sub>2</sub> = 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 p-value for testing the significance of the regression model is Also provided are SSR = 60 and SST = 180. -Refer to Exhibit 16-4. The p-value for testing the significance of the regression model is

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Exhibit 16-2 In a regression model involving 30 observations, the following estimated regression equation was obtained. Exhibit 16-2 In a regression model involving 30 observations, the following estimated regression equation was obtained.   For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 16-2. The p-value for testing the significance of the regression model is For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 16-2. The p-value for testing the significance of the regression model is

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A regression model relating the yearly income (Y), age (X1), and the gender of the faculty member of a university (X2 = 1 if female and 0 if male) resulted in the following information. A regression model relating the yearly income (Y), age (X<sub>1</sub>), and the gender of the faculty member of a university (X<sub>2</sub> = 1 if female and 0 if male) resulted in the following information.      a.Is gender a significant variable? b.Determine the multiple coefficient of determination. A regression model relating the yearly income (Y), age (X<sub>1</sub>), and the gender of the faculty member of a university (X<sub>2</sub> = 1 if female and 0 if male) resulted in the following information.      a.Is gender a significant variable? b.Determine the multiple coefficient of determination. a.Is gender a significant variable? b.Determine the multiple coefficient of determination.

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Exhibit 16-2 In a regression model involving 30 observations, the following estimated regression equation was obtained. Exhibit 16-2 In a regression model involving 30 observations, the following estimated regression equation was obtained.   For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 16-2. The degrees of freedom associated with SST are For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 16-2. The degrees of freedom associated with SST are

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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. 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 (X<sub>1</sub>), and whether or not agent X<sub>2</sub> (a proposed life extending agent) was added to the rats diet (X<sub>2</sub> = 0 if agent X<sub>2</sub> was not added, and X<sub>2</sub> = 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. From the above function, it can be said that the life expectancy of rats that were given agent X<sub>2</sub> is Also provided are SSR = 60 and SST = 180. -Refer to Exhibit 16-4. From the above function, it can be said that the life expectancy of rats that were given agent X2 is

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A regression analysis was applied in order to determine the relationship between a dependent variable and 8 independent variables. The following information was obtained from the regression analysis. R Square = 0.80 SSR = 4,280 Total number of observations n = 56 a.Fill in the blanks in the following ANOVA table. b.Is the model significant? Let α\alpha = 0.05.  A regression analysis was applied in order to determine the relationship between a dependent variable and 8 independent variables. The following information was obtained from the regression analysis. R Square = 0.80 SSR = 4,280 Total number of observations n = 56 a.Fill in the blanks in the following ANOVA table. b.Is the model significant? Let  \alpha  = 0.05.

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Serial correlation is

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Exhibit 16-1 In a regression analysis involving 25 observations, the following estimated regression equation was developed. 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<sub>b1</sub> = 3 S<sub>b2</sub> = 6 S<sub>b3</sub> = 7 SST = 4,800 SSE = 1,296 -Refer to Exhibit 16-1. The p-value for testing the significance of the regression model is 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 16-1. The p-value for testing the significance of the regression model is

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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. 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 (X<sub>1</sub>), and whether or not agent X<sub>2</sub> (a proposed life extending agent) was added to the rats diet (X<sub>2</sub> = 0 if agent X<sub>2</sub> was not added, and X<sub>2</sub> = 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 3 units of protein daily, and who took agent X<sub>2</sub> is 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

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Monthly total production costs and the number of units produced at a local company over a period of 10 months are shown below. Monthly total production costs and the number of units produced at a local company over a period of 10 months are shown below.    a.Draw a scatter diagram for the above data. b.Assume that a model in the form of   best describes the relationship between X and Y. Estimate the parameters of this curvilinear regression equation. a.Draw a scatter diagram for the above data. b.Assume that a model in the form of Monthly total production costs and the number of units produced at a local company over a period of 10 months are shown below.    a.Draw a scatter diagram for the above data. b.Assume that a model in the form of   best describes the relationship between X and Y. Estimate the parameters of this curvilinear regression equation. best describes the relationship between X and Y. Estimate the parameters of this curvilinear regression equation.

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The range of the Durbin-Watson statistic is between

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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 95% confidence, determine whether or not the third independent variable contributes significantly to the model.

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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. 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 (X<sub>1</sub>), and whether or not agent X<sub>2</sub> (a proposed life extending agent) was added to the rats diet (X<sub>2</sub> = 0 if agent X<sub>2</sub> was not added, and X<sub>2</sub> = 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 degrees of freedom associated with SSE are Also provided are SSR = 60 and SST = 180. -Refer to Exhibit 16-4. The degrees of freedom associated with SSE are

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Exhibit 16-2 In a regression model involving 30 observations, the following estimated regression equation was obtained. Exhibit 16-2 In a regression model involving 30 observations, the following estimated regression equation was obtained.   For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 16-2. The value of MSR is For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 16-2. The value of MSR is

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