Exam 29: Models for Decision Making

A large pharmaceutical company selected a random sample of new hires and Obtained their job performance ratings based on their first six months with the company. These data were used to build a multiple regression model to predict the job performance Of new hires based on age, GPA and gender (female = 1 and male = 0). The results of The analysis are shown below. How much of the variability in Job Performance is Explained by the regression model? The regression equation is Job Performance $= - 60.8 + 4.80$ Age $+ 1.44$ GPA $+ 9.06$ Gender Predictor Coef SE Coef T P Constant -60.76 22.49 -2.70 0.012 Age 4.802 1.177 4.08 0.000 GPA 1.443 2.379 0.61 0.549 Gender 9.060 2.314 3.92 0.001 $S = 5.56691 \quad \mathrm { R } - \mathrm { Sq } = 77.7 \%$

The time series graph below shows annual sales figures (in thousands of dollars) For a well known department store chain. The dominant component in these data is

Data were collected for a sample of 12 pharmacists to determine if years of Experience and salary are related. Below are the regression analysis results. The Dependent variable is Salary in thousands of dollars. How much of the variability in Pharmacists' salary is accounted for by years of experience? Regression Analysis: Salary versus Years Experience The regression equation is Salary $= 37.2 + 1.49$ Years Experience Predictor Coef SE Coef T P Constant 37.164 3.381 Years Experience 1.4882 0.2149 $S=5.58485 \quad R-S q=82.8\%$

A linear regression model was fit to data collected over a 13 year period Representing technology adoption over time. Based on the regression output below, the Durbin Watson statistic indicates Regression Analysis: Technology Adoption versus Time The regression equation is Technology Adoption $= - 11.9 + 3.37$ Time Predictor Coef SE Coef T P Constant -11.935 3.711 -3.22 0.008 Time 3.3709 0.4676 7.21 0.000 $S = 6.30783 \quad \mathrm { R } - \mathrm { Sq } = 82.5 \%$ Durbin-Watson statistic $= 0.278634$

A large pharmaceutical company selected a random sample of new hires and Obtained their job performance ratings based on their first six months with the company. These data were used to build a multiple regression model to predict the job performance Of new hires based on age, GPA and gender (female = 1 and male = 0). The regression Equation is: $\text { Job Performance } = - 60.8 + 4.80 \text { Age } + 1.44 \text { GPA } + 9.06 \text { Gender. }$ Which of the following is the correct interpretation for the regression coefficient of Gender?

A first-order autoregressive model, AR (1) was fit to monthly closing stock Prices, adjusted for dividends, of Boeing Corporation from January 2006 through August 2008 (closing price on the first trading day of the month). Based on the results shown Below, the forecast a month in which the previous month's closing price was $67.52 is Final Estimates of Parameters Type Coef SE Coef T P AR 1 0.9098 0.0969 9.39 0.000 Constant 6.835 1.207 5.67 0.000

Which of the following measures is used to check for collinearity when building a Multiple regression model?

Stock prices and earnings per share (EPS) data were collected for a sample of 15 Companies. Below are the regression results. Which of the following statement is true About the correlation between stock price and EPS? The regression equation is Stock Price $= - 0.49 + 14.8$ EPS Predictor Coef SE Coef T P Constant -0.486 4.032 -0.12 0.906 EPS 14.8129 0.9437 15.70 0.000 $S = 7.63235 \quad \mathrm { R } - \mathrm { Sq } = 95.0\%$

The regression model developed to predict a firm's Price-Earnings Ratio (PE) Based on Growth Rate, Profit Margin, and whether or not the firm is Green (1 = Yes, 0 = no. is $\mathrm { PE } = 8.04 + 0.757 \text { Growth Rate } + 0.0516 \text { Profit Margin } + 2.09 \text { Green? }$ Which of the following is the correct interpretation for the regression coefficient of Green?

If the point in the upper left corner of the scatterplot shown below is removed, What will happen to the correlation (r) and the slope of the line of best fit (b)?

The following is output from regression analysis performed to develop a model For predicting a firm's Price-Earnings Ratio (PE) based on Growth Rate, Profit Margin, And whether or not the firm is Green (1 = Yes, 0 = No). At = .05 we can conclude that ? The regression equation is $\mathrm { PE } = 8.04 + 0.757$ Growth Rate $+ 0.0516$ Profit Margin $+ 2.09$ Green? Predictor Coef SE Coef T P Constant 8.043 1.570 5.12 0.000 Growth Rate 0.7569 0.1355 5.59 0.000 Profit Margin 0.05162 0.03239 1.59 0.139 Green? 2.0900 0.7945 2.63 0.023 $S = 1.12583 \quad \mathrm { R } - \mathrm { Sq } = 87.8\%$

A large pharmaceutical company selected a random sample of new hires and Obtained their job performance ratings based on their first six months with the company. These data were used to build a multiple regression model to predict the job performance Of new hires based on age, GPA and gender (female = 1 and male = 0). The results of The analysis are shown below. At = .05 we can conclude that ? The regression equation is Job Performance $=-60.8+4.80$ Age $+1.44 \mathrm{GPA}+9.06$ Gender Predictor Coef SE Coef T P Constant -60.76 22.49 -2.70 0.012 Age 4.802 1.177 4.08 0.000 GPA 1.443 2.379 0.61 0.549 Gender 9.060 2.314 3.92 0.001 $\mathrm{S}=5.56691 \quad \mathrm{R}-\mathrm{Sq}=77.7 \%$

Quarterly returns were forecasted for a mutual fund comprised of technology Stocks. The forecast errors for the last six quarters are as follows: -.47, 1.12, -.85, 1.27, )07, and -.05. The MAD based on these forecast errors is

In order to examine if the size of cash bonuses depends on pay scale, data were Obtained on the average annual cash bonus and the average annual pay for a sample of 20 Companies. A regression model was fit to these data. From its plot of residuals versus Fitted values shown below, which assumption appears to be violated?

For many countries tourism is an important source of revenue. Data are collected On the number of foreign visitors to a country (in millions) and total tourism revenue (in Billions of dollars) for a sample of 10 countries. Below is partial regression analysis Output with tourism revenue as the dependent variable. The calculated t-statistic to test Whether the regression slope is significant is Regression Analysis: Tourism ($ bill) versus Visitors (mill) The regression equation is Tourism $(\$$ bill $)=21.5+0.295$ Visitors (mill) Predictor Coef sE Coef T P Constant 21.464 3.462 Visitors (mil1) 0.29497 0.07917 $S=2.58307 \quad \mathrm{R}-\mathrm{Sq}=63.4\%$

In order to examine if there is a relationship between the size of cash bonuses and Pay scale, data were obtained on the average annual cash bonus and the average annual Pay for a sample of 20 companies. Below is the regression analysis output with annual Cash bonus as the dependent variable. What is the correlation between average annual Cash bonus and average annual pay? Regression Analysis: Cash Bonus versus Pay The regression equation is Cash Bonus $=-4877+0.245$ Pay Predictor Coef SE Coef T P Constant -4877 9106 -0.54 0.599 Pay 0.2453 0.1079 2.27 0.036 $\mathrm{S}=13188.6 \quad \mathrm{R}-\mathrm{Sq}=22.3\%$

Weekly commodity prices for heating oil (in cents) were obtained and regressed Against time. The residual plots from fitting the linear model are shown below. Which Assumptions appear to be violated?

Which statement about influential points is true? I. Removal of an influential point changes the regression line. II. A high leverage point is always influential. III. Influential points have large residuals.