Exam 19: Data

Apply principles of the multiple regression model building process. -A sample of 30 companies was randomly selected for a study investigating what Factors affect the size of company bonuses. Data were collected on the number of Employees at the company and whether or not the employees were unionized (1 = yes, 0 = no). Multiple regression output is shown below for two competing models. Which Of the following statements is true? Dependent Variable is Average Annual Bonus Predictor Coef SE Coef T P Constant 347.9 872.2 0.40 0.693 Employees 0.6547 0.1105 5.92 0.000 Union 1259.5 605.8 2.08 0.047 S=1631.56-=62.48-()=59.6\% Dependent Variable is Average Annual Bonus Predictor Coef SE Coef T P Constant -1241.0 982.3 -1.26 0.218 Employees 0.8872 0.1318 6.73 0.000 Union 5253 1579 3.33 0.003 Emp*Union -0.05424 0.02012 -2.70 0.012 S=1469.91-=70.68-()=67.2\%

Use indicator (dummy) variables in multiple regression. -A sample of firms was selected from the high tech industry (Industry = 1) and the Financial services sector (Industry = 0). Data were collected on the following variables: Turnover rate, job growth, number of employees, and innovative index (higher scores Indicate a more innovative and creative organizational culture). Below are the multiple Regression results. The correct interpretation of the coefficient of Industry is Dependent Variable is Turnover Rate Predictor Coef SE Coef Constant 9.2439 0.7871 11.74 0.000 Innovative Index -0.02402 0.01524 -1.58 0.134 Job Growth -0.50127 0.07287 -6.88 0.000 Employees 0.0006144 0.0005461 1.13 0.276 Industry -2.8329 0.4699 -6.03 0.000 $S = 0.739664 \quad \mathrm { R } - \mathrm { Sq } = 95.6 \% \quad \mathrm { R } - \mathrm { Sq } ( \mathrm { adj } ) = 94.6 \%$

Interpret multiple regression output. -A sample of 30 companies was randomly selected for a study investigating what Factors affect the size of company bonuses. Data were collected on the number of Employees at the company and whether or not the employees were unionized (1 = yes, 0 = no). The multiple regression output including a plot of residuals versus fitted values Is shown below. Based on the results shown, which of the following statements is true? Dependent Variable is Average Annual Bonus Predictor Coef SE Coef T P Constant -1241.0 982.3 -1.26 0.218 Employees 0.8872 0.1318 6.73 0.000 Union 5253 1579 3.33 0.003 Emp*Union -0.05424 0.02012 -2.70 0.012

Use indicator (dummy) variables in multiple regression. -A sample of 30 companies was randomly selected for a study investigating what Factors affect the size of company bonuses. Data were collected on the number of Employees at the company and whether or not the employees were unionized (1 = yes, 0 = no). The following multiple regression model was fit to the data. The correct Interpretation of the regression coefficient of Union is Dependent Variable is Average Annual Bonus Predictor Coef SE Coef T P Constant 347.9 872.2 0.40 0.693 Employees 0.6547 0.1105 5.92 0.000 Union 1259.5 605.8 2.08 0.047

Adjust for different slopes using interaction terms in multiple regression. -A sample of 30 companies was randomly selected for a study investigating what Factors affect the size of company bonuses. Data were collected on the number of Employees at the company and whether or not the employees were unionized (1 = yes, 0 = no). The following multiple regression model was fit to the data. Based on this Model, what is the annual average bonus for a company with 5000 employees that are Unionized? Dependent Variable is Average Annual Bonus Predictor Coef SE Coef T P Constant -1241.0 982.3 -1.26 0.218 Employees 0.8872 0.1318 6.73 0.000 Union 5253 1579 3.33 0.003 Emp*Union -0.05424 0.02012 -2.70 0.012

Adjust for different slopes using interaction terms in multiple regression. -A sample of 30 companies was randomly selected for a study investigating what Factors affect the size of company bonuses. Data were collected on the number of Employees at the company and whether or not the employees were unionized (1 = yes, 0 = no). The following multiple regression model was fit to the data. Based on this Model, what is the annual average bonus for a company with 7500 employees that are not Unionized? Dependent Variable is Average Annual Bonus Predictor Coef SE Coef T P Constant -1241.0 982.3 -1.26 0.218 Employees 0.8872 0.1318 6.73 0.000 Union 5253 1579 3.33 0.003 Emp*Union -0.05424 0.02012 -2.70 0.012

Interpret output from automatic multiple regression model building procedures. -A sample of 22 firms was selected from the high tech industry (Industry = 1) and the Financial services sector (Industry = 0). Data were collected on the following variables: Turnover rate, job growth, number of employees, and innovative index (higher scores Indicate a more innovative and creative organizational culture). Below are the stepwise Regression results considering all predictor variables to explain Turnover Rate. The Resulting multiple regression model is Stepwise Regression: Turnover Rat versus Innovative I, Job Growth, ... Alpha-to-Enter: $0.15$ Alpha-to-Remove: $0.15$ Response is Turnover Rate on 4 predictors, with $\mathrm { N } = 22$ Step 1 2 3 Constant 8.603 8.838 9.841 Job Growth -0.868 -0.574 -0.500 T-Value -8.40 -8.58 -6.82 P-Value 0.000 0.000 0.000 Industry -3.14 -2.70 T-Value -7.41 -5.89 P-Value 0.000 0.000 Innovative Index -0.028 T-Value -1.91 P-Value 0.072 S 1.53 0.796 0.745 - 77.91 94.32 95.28 - (adj) 76.81 93.73 94.50 Mallows Cp 67.5 6.0 4.3

Use indicator (dummy) variables in multiple regression. -A sample of firms was selected from the high tech industry (Industry = 1) and the Financial services sector (Industry = 0). Data were collected on the following variables: Turnover rate, job growth, number of employees, and innovative index (higher scores Indicate a more innovative and creative organizational culture). What does the scatterplot Below suggest about developing a multiple regression model to predict turnover rate?

Adjust for different slopes using interaction terms in multiple regression. -A sample of 30 companies was randomly selected for a study investigating what Factors affect the size of company bonuses. Data were collected on the number of Employees at the company and whether or not the employees were unionized (1 = yes, 0 = no). What does the scatterplot of these data (shown below) suggest?

Apply principles of the multiple regression model building process. -Which of the following statements about building multiple regression models is true?

Check for collinearity among predictor variables in multiple regression. -A sample of 22 firms was selected from the high tech industry (Industry = 1) and the Financial services sector (Industry = 0). Data were collected on the following variables: Turnover rate, job growth, number of employees, and innovative index (higher scores Indicate a more innovative and creative organizational culture). A multiple regression Model is developed to predict Turnover Rate. However, to check for the possibility of Collinearity, a regression among just the predictor variables was run. Based on the results Shown below, the Variance Inflation Factor (VIF) for the predictor variable Innovative Index is The regression equation is Innovative Index $=40.9+3.99$ Job Growth -0.00612 Employees Predictor Coef SE Coef T P Constant 40.932 8.162 5.01 0.000 Job Growth 3.9863 0.8912 4.47 0.000 Employees -0.006123 0.009296 -0.66 0.518 $S=13.1511 \quad R-S q=52.5 \%$

Use indicator (dummy) variables in multiple regression. -A sample of 22 firms was selected from the high tech industry (Industry = 1) and the Financial services sector (Industry = 0). Data were collected on a number of variables in An attempt to develop a model to predict Turnover Rate (%). The final model deemed Most appropriate includes two predictor variables: Job Growth (%) and Industry. The Results are shown below. The predicted turnover rate for a firm in the financial services Sector with a 2% job growth rate is Dependent Variable is Turnover Rate Predictor Coef SE Coef T P Constant 8.8384 0.2776 31.83 0.000 Job Growth -0.57358 0.06686 -8.58 0.000 Industry -3.1395 0.4236 -7.41 0.000 $S = 0.795553 \quad R - S q = 94.3 \% \quad R - S q ( \operatorname { adj } ) = 93.7 \%$

Check for collinearity among predictor variables in multiple regression. -A sample of 22 firms was selected from the high tech industry (Industry = 1) and the Financial services sector (Industry = 0). Data were collected on the following variables: Turnover rate, job growth, number of employees, and innovative index (higher scores Indicate a more innovative and creative organizational culture). A multiple regression Model is developed to predict Turnover Rate. However, to check for the possibility of Collinearity, a regression among just the predictor variables was run. Based on the results Shown below, the Variance Inflation Factor (VIF) for the predictor variable Employees is The regression equation is Employees $= 972 - 7.13$ Innovative Index $+ 1.5$ Job Growth $+ 215$ Industry Predictor Coef SE Coef T P Constant 972.4 250.7 3.88 0.001 Innovative Index -7.134 6.360 -1.12 0.277 Job Growth 1.54 31.45 0.05 0.961 Industry 215.1 196.3 1.10 0.288 $S = 319.230 \quad R - S q = 8.8 \%$