2015spring-exam1-solutions.pdf - ISyE4031-B Regression and...

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ISyE4031 - B Regression and Forecasting Exam 1 Solutions Spring 2015 1. a. 1 ˆ = SS xy / SS xx => SS xx = - 59.27/ - 2.33 = 25.438 b. y = 40.8571. Since 0 ˆ = y - 1 ˆ x , x = (48.013 40.8571)/2.33 = 7.1559/2.33 = 3.071. 2. The regression equation is Y = 12.9 + 2.34 X Predictor Coef SE Coef T P Constant 12.9 1.032 a = 12.5 0.001 X 2.34 0.1150 20.387 0.001 S = b = 1.4811 R-Sq = 98.1% R-Sq(adj) = 97.9% Analysis of Variance Source DF SS MS F P Regression 1 912.43 912.43 415.913 0.000 Residual Error 8 17.55 2.1938 Total 9 929.98 a. t = 12.9/1.032 = 12.5. b. b = S = MSE = 8 / SSE = 1938 . 2 = 1.4811. 3. Least squares estimator: i n i i i n i i i x x a y x a y 1 1 2 ) ˆ ( 2 ) ˆ ( ˆ = 0 Upon setting the derivative to zero, we obtain i i i i y x x x a 2 ˆ Therefore, 2 2 ) ( ˆ i i i i i i i x a y x x x a y x . When a = 0, this estimator is equivalent to the slope estimator of the no-intercet model, i.e., 1 ˆ = n i i i y x 1 / n i i x 1 2 . 4. a. We test H 0 : 1 = 2 = 3 = 0 vs. H a : at least one is not 0. Since F (model) = 24.02 > F .05,3,16 = 3.24, we reject
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