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

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

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