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Unformatted text preview: STAT5044: Regression and ANOVA, Fall 2011 Exam 3 on Dec 02 Brief Solution Please make sure to specify all of your notations in each problem GOOD LUCK! 1 Problem# 1. The data consists of a sample branches of a large Australian bank (Cunning- ham and Heathcote, 1989). Each branch makes transactions of two types, and for each of the branches we have recorded the number of transactions T 1 and T 2 , as well as Time , the total number of minutes of labor used by the branch in type 1 and type 2 transactions. The data are displayed in Figure 1. • (1.a) What do the scatter plots (Figure 1) suggest about the relationships among Time , T 1 , and T 2 ? Explain in detail. The key features of the scatterplot matrix are: (1) the marginal response plots in the last row appear to have reasonably linear mean functions; (2) there appear to be a number of branches with no T 1 transactions but many T 2 transactions; and (3) in the plot of Time versus T 2 , variability appears to increase from left to right. • (1.b) Based on the scatter plots in (1.a), we first consider two simple linear regression models. We obtained R 2 = . 348 from the simple linear regression of time on T 1 and R 2 = . 459 from the simple linear regression of time on T 2 , respectively. What can be said about the proportion of variability on Time explained by T 1 and T 2 ? What about the total variation explained by both T 1 and T 2 About 46% of the variability in Time is explained by T2. T1 explains about 35% of the variability in Time. Total variation will be less than 46%+35% if the terms are related and are at least in part explaining the same variation. So total variation is between 0.459 and (0.459+0.35) Remark: the total can exceed the sum if the two variables act jointly so that knowing both gives more information than knowing just one of them....
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This note was uploaded on 01/02/2012 for the course STAT 5044` taught by Professor Staff during the Fall '11 term at Virginia Tech.
- Fall '11