420Pr4 - 1 Suppose the interaction model Y = 0 1 x1 2 x2 3...

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1. Suppose the interaction model Y = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 1 x 2 + ε was fit to n = 20 data points, and the following results were obtained: > sum( lm( y ~ 1 )$residuals^2 ) [1] 57 > sum( lm( y ~ x1 )$residuals^2 ) [1] 40 > sum( lm( y ~ x2 )$residuals^2 ) [1] 45 > sum( lm( y ~ x1 + x2 )$residuals^2 ) [1] 36 > sum( lm( y ~ x1 + x2 + I(x1*x2) )$residuals^2 ) [1] 30 a) Perform the significance of the regression test at α = 0.05. b) Do x 1 and x 2 interact? Perform the appropriate test at α = 0.05. c) Is there sufficient evidence to indicate that x 2 contributes information for the prediction of y ? Perform the appropriate test at α = 0.05. What is the p-value of this test?
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2. The grade point averages of students participating in college sports programs at Anytown State University are compared.* Football Basketball Hockey 3.2 2.6 2.4 2.4 1.9 3.8 3.1 2.6 3.7 3.3 2.8 2.3 1.8 2.5 2.1 1 y = 2.5 2 1 s = 0.220 2 y = 3.3 2 2 s = 0.235 3 y = 2.3 2 3 s = 0.145 a) At α
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420Pr4 - 1 Suppose the interaction model Y = 0 1 x1 2 x2 3...

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