A manufacturer of fancy scented bar soaps is interested in the price elasticity shown by her popular lilac variety. She assembled data for each of the past twenty months concerning the number of bars sold, the price, and the number of retail outlets that put the lilac soap on display and then carried out a regression analysis on this data. Here are the resulting means for each variable and the Excel output for the regression analysis:
Variable Mean
Bars of lilac soap sold €¦€¦€¦€¦€¦€¦€¦€¦. 2506
Price €¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦€¦ 1.59
Number of displays€¦€¦€¦€¦€¦€¦€¦€¦€¦. 167.9

(a) Find the coefficient of the price variable in the Excel output. Describe how you would explain the interpretation of this price coefficient to someone who is not familiar with multiple regression.
(b) Calculate the price elasticity implied by these results. Show your work.

Transcribed Image Text:

Regression Statistics Multiple F R Square Adjusted R Square Standard Error Observations ANOVA 0.855 0.731 0.699 291.738 20.000 df MS FSignificance F Regression 2.000 3931151.150 1965575.575 23.094 Residual 17.000 1446883.800 85110.812 Total 0.000 19.000 5378034.950 Coefficients Standard Error tStat Intercept 7376.431 1348.809 Price Displays -6.361 5.469 -6.753 -0.814 P-value 0.000 0.000 0.427 -1261.207 186.770 7.815