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STAT_371_Assignment_2_W_2013

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University of Waterloo Math-Business Program STAT 371: Statistics for Business 1 Assignment #2 Winter 2013 Dr. H. Fahmy The Assignment is due on (or before) Friday 15th of February, 2013 in my ma ... ilbox or in the bin (labeled STAT 371) next to o¢ ce 2001, M3 building, at 4:00 PM sharp. Instructions: Late assignments are not acceptable. All your answers should be justi…ed. Final answers without any justi…cations are worth zero points. 1. [12] LS Under Restriction. A regression equation is speci…ed as follows Yt = 1 + 2X2t + 3X3t + ut; t = 1; 2; :::; 30: Suppose that the following data, measured as deviations from sample means, are available: X x2 2 = 50; X x2 3 = 10; X y2 = 104 X x2x3 = 20; X yx2 = 40; X yx3 = 10: (a) [4.5] Estimate 2, 3, their standard errors, and R2: Are 2 and 3 statistically signi…cant? (b) [1.5] Test the hypothesis that 2 = 3: (c) [2] Re-estimate the coe¢ cients imposing the restriction that 2 = 3: (d) [2] Construct con…dence intervals for the restricted coe¢ cients. (e) [2] Test for the validity of the restriction. 2. [6] Consider the regression model Yt = 0 + 1X1t + 2X2t + 3X3t + ut; t = 1; 2; :::; n: Suppose that you have the following sums of squares and products of deviations from means for the n = 24 observations: X y2 = 60; X x2 1 = 10; X x2 2 = 30; X x2 3 = 20 X yx1 = 7; X yx2 = 7; X yx3 = 26 X x1x2 = 10; X x1x3 = 5; X x2x3 = 15: (a) [3] Test each of the following hypotheses 1 = 1; 2 = 1; 3 = 2; (b) [3] Test the hypothesis that 1 + 2 + 3 = 0: Explain how does this di¤er from the hypothesis that 1 2 3 = 1 1 2 ? Test the latter hypothesis. 3. [10] Consider the following regression model in deviation form yt = 1x1t + 2x2t + ut with sample data n = 10; X y2 = 493 3 ; X x2 1 = 30; X x2 2 = 3; X x1y = 30; X x2y = 20; X x1x2 = 0: [Show More]

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