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

The r 2 of 598 indicates that almost 60 of the

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The r 2 of .598 indicates that almost 60% of the variation of the sick days is accounted for by the hours of education. The standard error of the estimate is 2.455 days which is a modest error. The regression equation has an intercept of 7.75 which indicates that the model predicts that a worker will have an average of 7.75 sick days if the worker has participated in no hours of education. Notice the negative slope. As the number of hours of education increase, the regression model is deduct days from the intercept resulting in a prediction of fewer sick days. Shown below is a regression plot of this line and the data:
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Case Notes 35 2. The F value for the regression model indicates significant overall regression. The t -ratio, which here is the square root of F , also yields a p -value of .000 indicating that the population slope is different from zero. The value of r 2 = 90.1% is extremely high denoting a strong predictability in the model. The regression equation has a positive slope which indicates that the higher the satisfaction scores, the more sales there are.
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Case Notes 36 3. Shown below is Excel regression output for this problem. This output shows that hours of training is highly predictive of productivity ( r 2 = .976). The overall F value for this regression is extremely large and significant ( F = 662.28, p -value of .000000…). In addition, the standard error (1005.644) is quite small in relation to the five-figure productivity numbers that have a range of 20,000. The t test of the slope is also highly significant ( t = 179.65, p -value of .000000…) further underscoring the significance of hours of training as a predictor. Overall, this is a very strong regression model with much predictability. SUMMARY OUTPUT Regression Statistics Multiple R 0.988 R Square 0.976 Adjusted R Square 0.975 Standard Error 1005.644 Observations 18 ANOVA df SS MS F Significance F Regression 1 669781231.5 669781231.5 662.28 1.9027E-14 Residual 16 16181129.59 1011320.599 Total 17 685962361.1 Coefficients Standard Error t Stat P-value Intercept 70880.252 394.546 179.65 7.138E-28 Hours 5.093 0.198 25.73 1.903E-14
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Case Notes 37 Chapter 14 Starbucks Introduces Debit Card 1. This model uses four independent variables in an effort to predict the amount of money people spend on their debit card. Overall, the model has modest to good predictability with an R 2 of .755 and a standard error of $22.15. This standard error indicates that about 95% of the time, the model will be within + 2($22.15) or + $44.30 of the actual figurewhich is not particularly good.. While the overall test of the model is significant ( F = 15.38, p -value = .000007), an examination of the t tests and their associated p -values shows that only one of the predictors, income ( t = 6.69, p -value = .000002) is significant. None of the other variables are even close. Had a simple regression model been developed using just income to predict the amount of the prepaid card, the R 2 would be . 723, the t value for income would increase to 7.74, the standard error of the estimate would reduce to $21.96, and the overall F test would increase to 59.90.
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