Question

A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of 10 salespersons. Years of Experience Annual Sales ($1000s) Salesperson 80 100 119 138 153 166 168 171 180 194 The data on y = annual sales ($1000s) for new customer accounts and <= number of years of experience for a sample of 10 salespersons provided the estimated regression equation ý = 72.36 + 15.21x. For these data 7 = 4.9, (xi-)= 48.90, and s= 10.9441 a. Develop the 95% confidence interval for the mean annual sales for all salespersons with five years of experience. 11.60 ®, 18.82 ®) (to 2 decimals) b. The company is considering hiring Tom Smart, a salesperson with five years of experience. Develop a 95% prediction interval of annual sales for Tom Smart. 52.96 , 91.76 ) (to 2 decimals) c. Discuss the differences in your answers to parts (a) and (b). As expected, the prediction interval is much wider than the confidence interval. This is due to the fact that it is more difficult to predict annual sales for one new salesperson with 5 years of experience than it is to estimate the mean annual sales for all salespersons with 5 years of experience.

Answer 1

Solution:

We can use an excel regression data analysis tool to answer the given question. The excel output is given below:

Regression Analysis Regression Statistics Multiple R 0.960176666 R Square 0.921939231 Adjusted R Square 0.912181634 Standard Error 10.9441088 Observations 10 ANOVA df Significance F SS MS F Regression 1 11316.71186 11316.71186 94.48425752 1.04863E-05 Residual 958.1881391 119.7735174 Total 9 12274.9 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept Years of Experience 72.35787321 8.413465024 8.60024651 2.58477E-05 52.95638809 91.75935833 15.21267894 1.565041911 9.720301308 1.04863E-05 11.60368582 18.82167205 For Average Y Interval Half Width 7. Confidence Interval Lower Limit 140,43 Confidence Interval Upper Limit 156.41 For Individual Response Y Interval Half Width 26.47 Prediction Interval Lower Limit 121.95 Prediction Interval Upper Limit 174.89 CO

The data on y = annual sales ($1000s) for new customer accounts and e = number of years of experience for a sample of 10 salespersons provided the estimated regression equation ý = 72.36 + 15.212. For these data = 4.9, (x - E) = 48.90, and 8 10.9441 a. Develop the 95% confidence interval for the mean annual sales for all salespersons with five years of experience. ) (to 2 decimals) 140.43 156.41 b. The company is considering hiring Tom Smart, a salesperson with five years of experience. Develop a 95% prediction interval of annual sales for Tom Smart (to 2 decimals) 121.95 174.89 c. Discuss the differences in your answers to parts (a) and (b). As expected, the prediction interval is much wider than the confidence interval. This is due to the fact that it is to predict annual sales for one new salesperson with 5 years of experience than it is to estimate the more difficult mean annual sales for all salespersons with 5 years of experience.