An express delivery service the cost of a package (V), the package weight, the d

Question

An express delivery service the cost of a package (V), the package weight, the distance shipped, Twenty packages were randomly elected from among the large number received for shipment, and a detailed analysis of the shipping cost was conducted for each package. company recently conducted a study to investigate the relationship between A. estimate a simple linear regression model involving shipping and distance shipped. Interpret the slope coefficient of the least square line. The answer: For every additional mile the package is shipped, SHIPPING COSTS INCREASE BY $0.04 ALL OTHER THINGS EQUA B. IF the other explanatory variable -package weight-to the regression from the previous question. Estimate this expanded model. Based on your results, which model would you choose? 1. The results in the expanded model are more significant than in the first model. Therefore we should choose the second model 2. The first model has a higher coefficient for the distance shipped variable, therefore it should be chosen to fully account for this factor. 3. The R squared in the expanded model are higher than in the first model. Therefore it fits the data hetter and we should choose the expanded model 4. Both R squared and adjusted R squared in the expanded model are higher than in the first model. Therefore it fits the data better and we should choose the expanded model.

Explanation / Answer

A.

For increase of 1 mile in distance shipped, shipping costs would increase by $0.04 keeping all other factors constant

B.

1. The results in the expanded model are more significant than in the first model. Therefore, we should choose the second model.

First model SUMMARY OUTPUT Regression Statistics Multiple R 0.72266648 R Square 0.52224684 Adjusted R Square 0.495705 Standard Error 3.46398354 Observations 20 ANOVA df SS MS F Significance F Regression 1 236.100225 236.100225 19.67636 0.00031917 Residual 18 215.985275 11.999182 Total 19 452.0855 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -0.7334247 1.79207569 -0.4092599 0.68717769 -4.498436 3.03158659 -4.498436 3.03158659 Distance shipped 0.04451055 0.01003438 4.43580433 0.00031917 0.0234291 0.06559201 0.0234291 0.06559201 Expanded model SUMMARY OUTPUT Regression Statistics Multiple R 0.94683408 R Square 0.89649478 Adjusted R Square 0.8843177 Standard Error 1.65907854 Observations 20 ANOVA df SS MS F Significance F Regression 2 405.292293 202.646146 73.6214657 4.2382E-09 Residual 17 46.7932071 2.75254159 Total 19 452.0855 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -4.6390682 0.99240688 -4.6745627 0.00021765 -6.7328637 -2.5452727 -6.7328637 -2.5452727 Package weight 1.20722769 0.15398064 7.84012622 4.7993E-07 0.88235693 1.53209845 0.88235693 1.53209845 Distance shipped 0.03613542 0.00492327 7.33972436 1.1554E-06 0.02574824 0.04652261 0.02574824 0.04652261

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