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hw4 - Stat 704 Fall 2011 Homework 4 Due Thursday Oct 6...

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Stat 704, Fall 2011: Homework 4 Due Thursday Oct. 6 Carry out all hypothesis tests at the 5% significance level. 1. Consider the brand preference data of Problem 6.5. (a) Obtain and report the scatterplot matrix; what does it tell you about the re- lationship between ‘liking’ Y and each of the predictors x 1 ‘moisture’ and x 2 ‘sweetness’? (b) Fit the regression model Y i = β 0 + β 1 x i 1 + β 2 x i 2 + i . Report the ANOVA table and the table of regression effects. i. Using the p-value from the F-statistic in the ANOVA table, test H 0 : β 1 = β 2 = 0. What does this imply about β 1 and β 2 ? ii. Report each of b 1 and b 2 along with tests of H 0 : β 1 = 0 and β 2 = 0. Can either predictor be dropped in the presence of the other? iii. Intepret both estimated coefficients. (c) Obtain residual plots of e i vs. ˆ Y i , e i vs. x i 1 , and e i vs. x i 2 . Obtain the normal probability plot and a histogram of the residuals. What do these plots tell you?

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