Quiz3Soln

# Quiz3Soln - Y will increase 15.8 units 3 The test statistic...

This preview shows pages 1–2. Sign up to view the full content.

STA 3024 Introduction to Statistics 2 Quiz 3 with Solution Problem 1) Find the unknown a, b, c, d, e, f, g. (20 points) The regression equation is Y = 25.7 + 15.8 X Predictor Coef SE Coef T P Constant a 53.30 0.48 0.655 X b 4.499 3.51 0.025 Analysis of Variance Source DF SS MS F Regression c e f g Residual Error d 19496 Total 17 87021 2) Interpret the intercept and the slope.(10 points) 3) Test whether β = 0 using the one-sided test with the H 1 : β < 0. Given that α = 0 . 05. (20 points) 4) Find and interpret a 99% CI for β . (20 points) 5) Find the correlation, the coeﬃcient of determination. Interpret them. (10 points) 6) Test whether ρ = 0 (given α = 0 . 05). Is the conclusion consistent with your answer from part (2)? (20 points) Solution: 1) a = 25 . 7, b = 15 . 8, c = 1, d = 16, e = f = 67525, g = 55 . 41 2) The intercept is the predicted value of Y when X = 0. The slope equals to 15.8 which implies for every 1 unit increased in X, the predicted value for

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

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

Unformatted text preview: Y will increase 15.8 units. 3) The test statistic is t = 15 . 8 4 . 499 = 3 . 512 > 1 . 746 = t . 05 , 16 Thus, we reject the null ( H : β = 0) 1 4) Following the formula b ± t α 2 se b , we obtain the 99% CI to be 15 . 8 ± 2 . 921 * 4 . 499 = (2 . 658 , 28 . 942). We are 99% conﬁdent that the true value β falls between 2.658 and 28.942. 5) The correlation r = √ R 2 where R 2 = SS Regr SS Total = 67525 87021 = 0 . 776. Thus, r = 0 . 88. See notes for the interpretation. 6) The test statistic is t = . 88 q 1-. 776 16 = 7 . 43 > 1 . 746 = t . 05 , 16 Thus, we still reject H which is consistent with our part (3). This is a 1-sided test where H a : ρ < 0. 2...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

Quiz3Soln - Y will increase 15.8 units 3 The test statistic...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online