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Unformatted text preview: Stat 5102 (Geyer) Spring 2012 Homework Assignment 11 Due Wednesday, April 25, 2012 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 11-1. The data set in the URL http://www.stat.umn.edu/geyer/5102/data/prob11-1.txt has three variables x1 and x2 (the predictor variables) and y (the response variable). Fit three models to this data set (1) a linear model fitting a polynomial of degree one in the two predictor variables, (2) a quadratic model fitting a polynomial of degree two, and (3) a cubic model fitting a polynomial of degree three. Dont forget the terms of degree two and three containing products of powers of the two predictor variables. If you use the poly function, such terms are included automatically. Print out the ANOVA table for comparing these three models and in- terpret the P-values in the table. Which model would you say is the best fitting, and why? 11-2. The data set in the URL http://www.stat.umn.edu/geyer/5102/data/prob11-2.txt has two variables x (the predictor variable) and y (the response variable). As a glance at a scatter plot of the data done in R by plot(x, y) shows, the relationship between x and y does not appear to be linear. How- ever, it does appear that a so-called piecewise linear function with a knot at 11 may fit the data well. The means a function having the following three properties. It is linear on the interval x 11. It is linear on the interval x 11....
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