1. The managers at Reynolds Inc., a manufacturer of industrial scales and laboratory equipment, want to investigate the relationship between length of employment of their salespeople and the number of electronic laboratory scales sold. The following table presents the number of scales sold and the number of months employed by each of 15 randomly selected salespeople. Scales Months Sold Employed Salesperson Y X1 1 275 41 2 296 106 3 317 76 4 376 104 5 162 22 6 150 12 7 367 85 8 308 111 9 189 40 10 235 51 11 83 9 12 112 12 13 67 6 14 325 56 15 189 19 (a) Construct a scattergram between the number of scales sold (Y) and the number of months employed (X1). Does there appear to be a non-linear relationship? (b) Estimate a simple linear regression equation that could be used to predict the number of scales sold. Evaluate the estimated regression equation (Rsquare, Adjusted Rsquare, Regression Standard Error (SE), t-tests, etc.). (c) Create a second explanatory variable (X2) by squaring each value of the months employed variable (X1). (d) Estimate a non-linear (quadratic) multiple regression equation by including both the X1 and X2 explanatory variables in the model. Evaluate the estimated regression equation (Rsquare, Adjusted Rsquare, Regression Standard Error (SE), t-tests, F-Test etc.). (e) Which estimated regression equation provides a better fit to the data? Explain in detail. (f) Calculate the number of months employed by a salesperson that will maximize the number of scales sold using the estimated regression equation in part d. (g) How many scales will by sold at this maximizing point calculated in part f.
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