4. Stereo Ltd. is retailer of stereo components with numerous stores throughout

Question

4. Stereo Ltd. is retailer of stereo components with numerous stores throughout the Southwest. Stereo Ltd. desires a to develop a re sales staff that believes model a five predicting store which they plan to use in locating new stores. can be miles radius of store sales can be predicted the basis ofd) number of competitors constructed location. within this zone. The regression as: Where Store sales (Sten thousands) Xi-Number of in trading competitors Population trading zone (thousands) The staff of Stereo Ltd. has taken a random sample often company stores and obtained the data and statistics given in the following table. Variable Coefficient t Statistic intercept 3.417 Number of Competitors XI) bl 739 -2.048 Population o 2) Coefficient of determination 0,89 Est For Corrected coefficient of determination 0.87 3.86 4.74 A. Write the regression equation and describe the economic meaning ofcach individual independent variable included in the Stereo Ltd's sales equation. B. Interpret the coefficient of determination for the Stereo Ltd's sales equation. c considering its value would you drop any of the independent variables from consideration? (At 95%confidence level t critical 960 Explain. D. Predict the daily sales in a Dew trading zone with xi-4 andx2-34 E. To of the of the statistic, derive the 95 percent confidence interval for expected sales in the new trading zone level 1.96). F. Do you consider this model to be acceptable? Explain.

Explanation / Answer

e ) the equation is y = 13.41 -1.739 x1 +0.062x2

put x1 = 4 and x2 = 34

13.41 -1.739*4 +0.062*34 = 8.56

now the se is 2.39 and z = 1.96 for the 95% confidence interval ,

so we use

point+- z*SE for the confidence interval 8.56+-1.96*2.39

3.87 , 13.24

f) yes , as we see that the r2 value is 0.89 , hence model is able to capture 89% of the varation of the data. also , the corrected coefficient of correlation is 0.87, which captures 87% of the variation of the data. corrected correlation takes into account the number of predictors (x1,x2) used in the modeling process.

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