420Exam2Aans

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

This preview shows pages 1–3. Sign up to view the full content.

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 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online