420Exam2Aans - STAT 420 Exam 2 (Version A) (Answers) Fall...

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STAT 420 Fall 2007 Exam 2 ( Version A ) ( Answers ) 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 = 27 data points, and the following results were obtained: SYY = Σ ( y y ) 2 = 500 RSS = Σ ( y y ˆ ) 2 = 25 Coefficients: Estimate Std. Error (Intercept) 160.0 100.00 x1 0.2 0.04 x2 6.0 3.00 x1x2 10.0 4.00 a) (5) Is there evidence to indicate that x 1 and x 2 interact? Find the p-value of the appropriate test. H 0 : β 3 = 0 H a : β 3 0 Test Statistic: T = 00 . 4 0 . 10 = 2.50 . n p = 27 – 4 = 23 degrees of freedom P-value = two tails = 2 × ( Area to the right of T = 2.50 ) = 2 × 0.01 = 0.02 . b) (2) Based on the least squares estimates of the β parameters, give the estimate of the change in E ( Y ) for every 1-unit increase in x 1 , when x 2 = 4. ( β 1 + β 3 x 2 ) represents the change in E ( Y ) for every 1-unit increase in x 1 , holding x 2 fixed. β 1 + β 3 × 4 = 0.2 + 10 × 4 = 40.2 .
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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) (12) At α = 0.05, can one conclude that there is a difference in the mean GPA of the three groups? H
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420Exam2Aans - STAT 420 Exam 2 (Version A) (Answers) Fall...

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