Thank you Sample Data for Supermarket Profits. Store Size square feet) 35 Profit

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Sample Data for Supermarket Profits. Store Size square feet) 35 Profit dollars) 20 Supermarket Food Sales Nonfood Sales Number (tens of thousands (tens of thousands (thousands of (thousands of of dollars) of dollars) 35 98 83 76 93 305 130 189 175 101 269 421 195 282 203 15 27 16 28 46 56 12 40 32 16 27 35 57 3 1 92 23 10 1. Run a multiple regression using the above data. (with profit as the dependent variable). 2. Comparethe result of question (l) with anoher regression equation obtained withour the food sales variable 3. Which of the models do you prefer? Why? 4. Interpret your results for (1) and (2)

Explanation / Answer

Q1)

Q2) Without food sales variable

The equation which does not include food sales has R-square value 0.9721 whereas the full model has R-square value 0.9849. Here for reducing a covariate variable reduces 0.0128 in R-square and the covariate food sales do not have the significant effect on Profit at 0.05 level of significance. Hence, the model without food sales is best among these two model.

3) The model obtained without food sales is preferred.

4) Model 1 with food sales. The estimated p-value of food sales is 0.0658 Hence, this variable does not have the significant effect on profit at 0.05 level of significance. Whereas, the estimated p-value of nonfood sales and store size are 0.0182 and 0.0001 respectively. Hence, both the covariates have the significant effect on profit at 0.05 level of significance.

Model 2 without food sales. The estimated p-value of nonfood sales and store size are 0.1015 and 0.0001 respectively. Hence, the nonfood sales do not have the significant effect on profit at 0.05 level of significance whereas the store size has the significant effect at 0.05 level of significance.

SUMMARY OUTPUT Regression Statistics Multiple R 0.992398792 R Square 0.984855361 Adjusted R Square 0.977283042 Standard Error 1.249867779 Observations 10 ANOVA df SS MS F Significance F Regression 3 609.527 203.1757 130.0599 7.55516E-06 Residual 6 9.373017 1.562169 Total 9 618.9 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -10.17024332 3.473129 -2.92827 0.026346 -18.66868283 -1.6718038 Food Sales 0.027038115 0.012041 2.245505 0.065847 -0.002425142 0.056501372 Nonfood sales 0.097052345 0.030147 3.219291 0.018153 0.023284996 0.170819694 Store Size 0.524675168 0.059158 8.869011 0.000114 0.379920148 0.669430188

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