Exam 15: Multiple Regression

Use the following information for problems To determine what affects turnover rate, a sample of 33 companies was randomly selected and data collected on the average annual bonus and turnover rate (%). In addition, a questionnaire was administered to the employees of each company to arrive at a trust index (measured on a scale of 0 - 100). Below are the multiple regression results. Dependent Variable is Turnover Rate Predictor Coef SE Coef T P Constant 12.1005 0.7826 15.46 0.000 Trust Index -0.07149 0.01966 -3.64 0.001 Average Bonus -0.0007216 0.0001481 -4.87 0.000 $S = 1.49746 \quad \mathrm { R } - \mathrm { Sq } = 79.68 \quad \mathrm { R } - \mathrm { Sq } ( \mathrm { adj } ) = 78.3 \frac { 8 } { 8 }$ Analysis of Variance Source DF SS MS Regression 2 262.73 131.36 Residual Error 30 67.27 2.24 Total 32 330.00 -Write out the estimated regression equation.

A sample of 33 companies was randomly selected and data collected on the average annual bonus, turnover rate (%), and trust index (measured on a scale of 0 - 100). The regression coefficient associated with Average Bonus was found to be -0.0007216. The correct interpretation of this value is

Selling price and amount spent advertising were entered into a multiple regression to determine what affects flat panel LCD TV sales. The plot of residuals versus Predicted values is shown below. What does the residual plot suggest?

A sample of 33 companies was randomly selected and data collected on the average annual bonus, turnover rate (%), and trust index (measured on a scale of 0 - 100). Using the output below, and a significance level of α = .01, we can conclude that Dependent Variable is Turnover Rate Predictor Coef SE Coef T P Constant 12.1005 0.7826 15.46 0.000 Trust Index -0.07149 0.01966 -3.64 0.001 Average Bonus -0.0007216 0.0001481 -4.87 0.000 $S = 1.49746 \quad \mathrm { R } - \mathrm { Sq } = 79.6 \% \mathrm { R } - \mathrm { Sq } ( \mathrm { adj } ) = 78.3 \%$ Analysis of Variance Source DF SS MS Regression 2 262.73 131.36 Residual Error 30 67.27 2.24 Total 32 330.00

A sample of 33 companies was randomly selected and data collected on the average annual bonus, turnover rate (%), and trust index (measured on a scale of 0 - 100). According to the output is shown below, what is the estimated multiple regression Model? Dependent Variable is Turnover Rate Predictor Coef SE Coef T P Constant 12.1005 0.7826 15.46 0.000 Trust Index -0.07149 0.01966 -3.64 0.001 Average Bonus -0.0007216 0.0001481 -4.87 0.000

Use the following information for problems Sales figures (number of units), selling price and amount spent on advertising (as a percentage of total advertising expenditure in the previous quarter) for the popular Sony Bravia Television were obtained for last quarter from a sample of 30 different stores. The results of a multiple regression are presented below. Dependent Variable $1 \mathrm {~s}$ Sales Predictor Coef sE Coef T P Constant 90.19 25.08 3.60 0.001 Price =0.03055 0.01005 -3.04 0.005 Advertising 3.0926 0.3680 8.40 0.000 $S = 10.6075 \quad R - S q = 84.4 \leqslant \quad R - S q ( a d j ) = 83.3 \div \frac { 7 } { 6 }$ Analyaia of Variance Source DF SS MS Regresgion 2 16477.3 8238.7 Residual Error 27 3038.0 112.5 Total 29 19515.4 -Report the adjusted R2 for this model. Write a sentence interpreting this value.

Use the output to describe the relationship between sales figures, selling price and amount spent on advertising for the Sony Bravia. In 2-3 sentences, summarize the results of the multiple regression.

A sample of 33 companies was randomly selected and data collected on the average annual bonus, turnover rate (%), and trust index (measured on a scale of 0 - 100). Based on the output, how much of the variability in Turnover Rate is explained by the Estimated multiple regression model? Dependent Variable is Turnover Rate Predictor Coef SE Coef T P Constant 12.1005 0.7826 15.46 0.000 Trust Index -0.07149 0.01966 -3.64 0.001 Average Bonus -0.0007216 0.0001481 -4.87 0.000

Use the following information for problems To determine what affects turnover rate, a sample of 33 companies was randomly selected and data collected on the average annual bonus and turnover rate (%). In addition, a questionnaire was administered to the employees of each company to arrive at a trust index (measured on a scale of 0 - 100). Below are the multiple regression results. Dependent Variable is Turnover Rate Predictor Coef SE Coef T P Constant 12.1005 0.7826 15.46 0.000 Trust Index -0.07149 0.01966 -3.64 0.001 Average Bonus -0.0007216 0.0001481 -4.87 0.000 $S = 1.49746 \quad \mathrm { R } - \mathrm { Sq } = 79.68 \quad \mathrm { R } - \mathrm { Sq } ( \mathrm { adj } ) = 78.3 \frac { 8 } { 8 }$ Analysis of Variance Source DF SS MS Regression 2 262.73 131.36 Residual Error 30 67.27 2.24 Total 32 330.00 -State the hypotheses for testing the regression coefficient of Average Annual Bonus. Based on the results, what do you conclude?

Use the following information for problems Sales figures (number of units), selling price and amount spent on advertising (as a percentage of total advertising expenditure in the previous quarter) for the popular Sony Bravia Television were obtained for last quarter from a sample of 30 different stores. The results of a multiple regression are presented below. Dependent Variable $1 \mathrm {~s}$ Sales Predictor Coef sE Coef T P Constant 90.19 25.08 3.60 0.001 Price =0.03055 0.01005 -3.04 0.005 Advertising 3.0926 0.3680 8.40 0.000 $S = 10.6075 \quad R - S q = 84.4 \leqslant \quad R - S q ( a d j ) = 83.3 \div \frac { 7 } { 6 }$ Analyaia of Variance Source DF SS MS Regresgion 2 16477.3 8238.7 Residual Error 27 3038.0 112.5 Total 29 19515.4 -Write out the estimated regression equation.

Selling price and amount spent advertising were entered into a multiple regression to determine what affects flat panel LCD TV sales. Using the output below, estimate The number of units sold on average at a store that sells the Sony Bravia for $2199 And spends 10% of its advertising budget on the product. Dependent Variable is Sales Predictor Coef SE Coef T P Constant 90.19 25.08 3.60 0.001 Price -0.03055 0.01005 -3.04 0.005 Advertising 3.0926 0.3680 8.40 0.000

Use the following information for problems To determine what affects turnover rate, a sample of 33 companies was randomly selected and data collected on the average annual bonus and turnover rate (%). In addition, a questionnaire was administered to the employees of each company to arrive at a trust index (measured on a scale of 0 - 100). Below are the multiple regression results. Dependent Variable is Turnover Rate Predictor Coef SE Coef T P Constant 12.1005 0.7826 15.46 0.000 Trust Index -0.07149 0.01966 -3.64 0.001 Average Bonus -0.0007216 0.0001481 -4.87 0.000 $S = 1.49746 \quad \mathrm { R } - \mathrm { Sq } = 79.68 \quad \mathrm { R } - \mathrm { Sq } ( \mathrm { adj } ) = 78.3 \frac { 8 } { 8 }$ Analysis of Variance Source DF SS MS Regression 2 262.73 131.36 Residual Error 30 67.27 2.24 Total 32 330.00 -Using this model, the turnover rate for a company with a trust index score of 70 and an average annual bonus of $6500 is predicted to be 2.41%. If the company observes a turnover rate of 2.15%, what is the value of the residual for this company? What does the value of the residual tell you about the prediction?

Selling price and amount spent advertising were entered into a multiple regression to determine what affects flat panel LCD TV sales. If the scatterplots of sales versus Both selling price and amount spent on advertising are created, they are being used to Determine whether

Use the following information for problems To determine what affects turnover rate, a sample of 33 companies was randomly selected and data collected on the average annual bonus and turnover rate (%). In addition, a questionnaire was administered to the employees of each company to arrive at a trust index (measured on a scale of 0 - 100). Below are the multiple regression results. Dependent Variable is Turnover Rate Predictor Coef SE Coef T P Constant 12.1005 0.7826 15.46 0.000 Trust Index -0.07149 0.01966 -3.64 0.001 Average Bonus -0.0007216 0.0001481 -4.87 0.000 $S = 1.49746 \quad \mathrm { R } - \mathrm { Sq } = 79.68 \quad \mathrm { R } - \mathrm { Sq } ( \mathrm { adj } ) = 78.3 \frac { 8 } { 8 }$ Analysis of Variance Source DF SS MS Regression 2 262.73 131.36 Residual Error 30 67.27 2.24 Total 32 330.00 -Is the regression equation significant overall? Explain.

Use the following information for problems Sales figures (number of units), selling price and amount spent on advertising (as a percentage of total advertising expenditure in the previous quarter) for the popular Sony Bravia Television were obtained for last quarter from a sample of 30 different stores. The results of a multiple regression are presented below. Dependent Variable $1 \mathrm {~s}$ Sales Predictor Coef sE Coef T P Constant 90.19 25.08 3.60 0.001 Price =0.03055 0.01005 -3.04 0.005 Advertising 3.0926 0.3680 8.40 0.000 $S = 10.6075 \quad R - S q = 84.4 \leqslant \quad R - S q ( a d j ) = 83.3 \div \frac { 7 } { 6 }$ Analyaia of Variance Source DF SS MS Regresgion 2 16477.3 8238.7 Residual Error 27 3038.0 112.5 Total 29 19515.4 -Predict the sales for a store that sells the Sony Bravia for $2199 and spends 10% of its advertising budget on the product.

Use the following information for problems Sales figures (number of units), selling price and amount spent on advertising (as a percentage of total advertising expenditure in the previous quarter) for the popular Sony Bravia Television were obtained for last quarter from a sample of 30 different stores. The results of a multiple regression are presented below. Dependent Variable $1 \mathrm {~s}$ Sales Predictor Coef sE Coef T P Constant 90.19 25.08 3.60 0.001 Price =0.03055 0.01005 -3.04 0.005 Advertising 3.0926 0.3680 8.40 0.000 $S = 10.6075 \quad R - S q = 84.4 \leqslant \quad R - S q ( a d j ) = 83.3 \div \frac { 7 } { 6 }$ Analyaia of Variance Source DF SS MS Regresgion 2 16477.3 8238.7 Residual Error 27 3038.0 112.5 Total 29 19515.4 -State the hypotheses for testing the regression coefficient of Price. Based on the results, what do you conclude?