Simple Regression Assignment Answers 1. Data were collected to explain the satisfaction rating a caller gives a customer representative based on the amount of time the caller is on hold (hold time is expressed in minutes) Complete the Table Below Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.661 10 ANOVA df Regression Residual Total Intercept Hold time Coefficients 23.90 -1.30 SS 58.7 25.3 Standard Error 4.430 0.303 MS F t Stat P-value 0.0006499 0.003 Significance F 0.0026 Lower 95% Based on the regression results, answer the following questions a) What is the estimated regression equation? b) What percentage of the variation in the rating is explained by hold time? c) What is the standard error of the error term in the regression equation? d) Is the variable \"hold time\" significant at the 10% level of significance? How do you know? e) What is the predicted rating if a caller is on hold for 10 minutes? Simple Regression Assignment Problems 1 Upper 95% f) What is the effect on rating of increasing the hold time by 1 minute? g) What is the 95% confidence interval for the coefficient of hold time? Simple Regression Assignment Problems 2 2) Data were collected to explain the an employee's annual income raise (expressed in $'s) based on the employee's rating (on a scale of 1-20) Complete the Table Below Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.709 8 ANOVA df Regression Residual Total Intercept rating Coefficients -201.5 146.5 SS 726978.8 241771.2 Standard Error 543.6 34.5 MS F 18.0 Significance F 0.005394931 t Stat P-value 0.724 0.005 Lower 95% Upper 95% Based on the regression results, answer the following questions a) What is the estimated regression equation? b) What percentage of the variation in raises is explained by rating? c) What is the correlation between rating and raise? d) What is the standard error of the error term in the regression equation? e) Is the variable \"rating\" significant at the 1% level of significance? How do you know? Simple Regression Assignment Problems 3 f) What is the predicted raise for someone with an 18 rating? g) What is the effect on \"raise\" of getting a 1 point higher rating? h) What is the 95% confidence interval for the coefficient of rating? Simple Regression Assignment Problems 4 3) Data were collected to explain the amount of a customer's purchase (expressed in $'s) based on the amount of time the customer has spent on the company's website (expressed in minutes) Complete the Table Below Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.508 12 ANOVA df Regression Residual Total Intercept Time Coefficients -3.53 7.12 SS 63067.3 51086.4 Standard Error 42.21 2.03 MS F Significance F 0.005598142 t Stat P-value 0.935 0.006 Lower 95% Upper 95% Based on the regression results, answer the following questions a) What is the estimated regression equation? b) What percentage of the variation in purchase amount is explained by time? c) What is the correlation between purchase amount and time? d) What is the standard error of the error term in the regression equation? e) Is the variable \"time\" significant at the 5% level of significance? How do you know? f) What is the predicted purchase amount for a customer who has spent 30 minutes on the website? Simple Regression Assignment Problems 5 Simple Regression Assignment Problems 6 4) Data were collected to explain the number of wins an NFL team has based on the average points per game that they score (PPG) Complete the Table Below Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.571 11 ANOVA df Regression Residual Total Intercept PPG Coefficients -6.758 0.673 SS 68.0 42.7 Standard Error 3.835 0.178 MS F Significance F 0.00430874 t Stat P-value 0.112 0.004 Lower 95% Upper 95% Based on the regression results, answer the following questions a) What is the estimated regression equation? b) What percentage of the wins is explained by PPG? c) What is the standard error of the error term in the regression equation? d) Is the variable \"PPG\" significant at the 1% level of significance? How do you know? e) What is the predicted number of wins for a team that averages scoring 28 points per game? f) What is the effect on wins of increasing the average PPG by 1? Simple Regression Assignment Problems 7 5) Data were collected to explain the number of wins a major league baseball team has based on the earned run average (ERA) of the team's starting pitchers Complete the Table Below Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.707 8 ANOVA df Regression Residual Total Intercept ERA Coefficients 165.46 -21.48 SS 770.17 257.83 Standard Error 21.38 5.07 MS F Significance F 0.005478716 t Stat P-value 0.000 0.005 Lower 95% Upper 95% Based on the regression results, answer the following questions a) What is the estimated regression equation? b) What percentage of the variation in wins is explained by ERA? c) What is the correlation between wins and ERA? d) What is the standard error of the error term in the regression equation? e) Is the variable \"ERA\" significant at the 10% level of significance? How do you know? f) What is the predicted number of wins for a team with an ERA of 3.50? Simple Regression Assignment Problems 8 g) What is the effect on wins of decreasing the ERA by 1 run? Simple Regression Assignment Problems 9