185323959-Business-Stats-Ken-Black-Case-Answers.pdf

Summary output regression statistics multiple r 0869

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SUMMARY OUTPUT Regression Statistics Multiple R 0.869 R Square 0.755 Adjusted R Square 0.706 Standard Error 22.1483 Observations 25 ANOVA df SS MS F Significance F Regression 4 30175.0423 7543.7606 15.38 0.000007 Residual 20 9810.9577 490.5479 Total 24 39986 Coefficients Standard Error t Stat P-value Intercept -83.826 22.494 -3.73 0.0013 Age 0.237 0.576 0.41 0.6852 Days 1.190 1.474 0.81 0.4291 Cups 1.422 2.631 0.54 0.5949 Income 2.407 0.360 6.69 0.000002
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Case Notes 38 2. This model attempts to predict the number of days per month that a customer frequents Starbucks. The predictor variables are age, income, and number of cups of coffee per day. The Excel results of this analysis are shown below. The model is modest to weak with an R 2 of just .416. The standard error of 3.28 days indicates that the model would predict within + 2(3.28) or + 6.56 days about 95% of the time. A perusal of the data shows that the range of number of days is 16 days. The relatively large size of the standard error to this range is further evidence of the model’s weakness. A study of the t statistics reveals that the predictor variable, cups, is the only significant predictor ( t = 3.40, p -value .0027). The number of cups of coffee that a person drinks per day seems to be a good predictor of the number of times per month the person frequents Starbucks. Heavy coffee drinkers come often (the coefficient indicates a positive relationship between cups and frequency). In attempting to increase store traffic, Starbucks could target their marketing efforts at the more heavy coffee drinkers or develop and market products that might lure lighter coffee drinkers to their outlets for different reasons. If a simple regression model is used to predict number of days by cups of coffee, the R 2 is .345 and the standard error is 3.32.
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Case Notes 39 SUMMARY OUTPUT Regression Statistics Multiple R 0.645 R Square 0.416 Adjusted R Square 0.332 Standard Error 3.2791 Observations 25 ANOVA df SS MS F Significance F Regression 3 160.7593 53.5864 4.98 0.0091 Residual 21 225.8007 10.7524 Total 24 386.56 Coefficients Standard Error t Stat P-value Intercept 5.9684 3.0651 1.95 0.0650 Cups 1.0644 0.3127 3.40 0.0027 Income 0.0716 0.0509 1.41 0.1742 Age -0.0785 0.0835 -0.94 0.3578
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Case Notes 40 3. Shown below is the output from an Excel multiple regression analysis to predict sales revenue by number of stores, number of drinks, and average weekly earnings. The predictability is extremely high with an R 2 of .9998. In predicting sales revenues that range from 400 to 2600, the standard error of the estimate is only 16.69. The overall F of 4539.21 is significant at alpha = .00001. While number of stores is not a significant predictor ( t = -0.95, p -value = .41145), both number of drinks ( t = -7.47, p -value = .00497) and average weekly earnings ( t = 13.70, p -value .00084) are significant at α = .01. Notice that for the predictor, number of drinks, both the t value and the coefficient are negative. This indicates that, at least in this model with other variables in the model, there is a negative relationship between number of drinks and sales revenue. However, a cursory examination of the raw data shows that as sales revenues increase so do the number of drinks. This points out one of the dangers in over interpreting the regression coefficients (discussed in Chapter 15 in section on multicollinearity).
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