invest_3ed.pdf

Do these transformed variables appear to be more

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versus explanatory variable). Do these transformed variables appear to be more suitable for the basic regression model? Explain. (f) Interpret the slope coefficient in the regression model using the log transformed variables. (g) Use the least squares regression line to predict the cost of a 3,000 square foot house. [ Hints : Substitute log 10 (3000) into the right hand side of the equation to obtain a prediction for the log 10 (price) , and then raise 10 to this power to determine the predicted price. Similarly, you can back transform the endpoints of the confidence and prediction intervals from R/Minitab.] Discussion: The log transformation has made improvements for both the normality condition and the equal variance condition . It is not uncommon for one transformation to “correct” more than one problem. We could continue to explore other transformations (e.g., square root and power transformations) until we find transformed data that are more appropriate for the basic regression model. Although these transformations are useful, we then have to be careful in how we interpret the regression coefficients and make predictions. If possible, it is usually most useful to “back - transform” to the original scale.

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Chance/Rossman, 2015 ISCAM III Investigation 5.14 400 Practice Problem 5.14 The datafile walmart.txt contains data on the number of stores and the number of SuperCenters that Wal-Mart had in operation between 1989 and 2002. (a) Create a scatterplot of the number of SuperCenters that Wal-Mart has had in operation versus time. (b) Would it be appropriate to use the basic regression model for these data? Explain. (c) Transform the SuperCenters variable by taking the square root. Would it be appropriate to use the basic regression model for the relationship between this variable and year? Explain. (d) Transform the SuperCenters variable by taking the natural log. Would it be appropriate to use the basic regression model for the relationship between this variable and year? Explain. (e) Choose the best model from either (c) or (d) (and justify your choice), find the least-squares regression equation and use it to predict how many SuperCenters Wal-Mart had in operation in 2003. (f) Report and interpret a 95% prediction interval for 2003. Summary of Inference for Regression To test H 0 : E 1 = hypothesized slope vs. H a : E 1 hypothesized slope The test statistic: t = ) ( 1 1 b SE slope d hypothsize b ± follows a t- distribution with df = n ± 2 An approximate 100 × C% confidence interval formula is b 1 + t n ± 2 SE( b 1 ) where ± t n ± 2 is the 100 × (1 ± C)/2 percentile of the student t- distribution with n ± 2 degrees of freedom. These procedures are valid as long as x L: There is a linear relationship between the response and explanatory variable. x I: The observations are independent. x N: The response follows a normal distribution for each value of x .
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