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Material Type: Assignment; Class: Applied Regression Analysis; Subject: STATISTICS; University: University of Wisconsin - Madison; Term: Spring 2004;

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Download Homework 3 Solutions | Applied Regression Analysis | STAT 333 and more Assignments Statistics in PDF only on Docsity! Stat 333 Spring 2004 2/27/2004 Homework 3 Solution 1. a. (yield)i = β0 + β1(rain)i + i. Y = 60 50 70 70 80 50 60 40 X = 1 8 1 10 1 11 1 10 1 9 1 9 1 12 1 11 Then X′Y = [ 480 4780 ] X′X = [ 8 80 80 812 ] (X′X)−1 = [ 203/24 −5/6 −5/6 1/12 ] ( or = [ 8.49 −0.83 −0.83 0.08 ]) β̂ = (X′X)−1X′Y = [ 76.67 −1.67 ] b. (yield)i = β0 + β1(rain)i + β2(temp)i + i. Y = 60 50 70 70 80 50 60 40 X = 1 8 56 1 10 47 1 11 53 1 10 53 1 9 56 1 9 47 1 12 44 1 11 44 Then X′Y = 4804780 24360 X′X = 8 80 40080 812 3970 400 3970 20180 (X′X)−1 = 10421/168 −55/21 −5/7−55/21 1/7 1/42 −5/7 1/42 1/105 or = 62.03 −2.62 −0.71−2.62 0.14 0.02 −0.71 0.03 0.01 β̂ = (X′X)−1X′Y = −144.765.71 2.95 Homework 3 Solution 1 Ting-Li Lin Stat 333 Spring 2004 2/27/2004 2. a. (distance)i = β0 + β1(height)i + i. Y = 253 337 395 451 495 534 573 X = 1 100 1 200 1 300 1 450 1 600 1 800 1 1000 Then X′Y = [ 3038 1711350 ] X′X = [ 7 3450 3450 2342500 ] (X′X)−1 = [ 0.521 −7.675× 10−4 −7.675× 10−4 1.557× 10−6 ] β̂ = (X′X)−1X′Y = [ 269.71 0.33 ] b. (distance)i = β0 + β1(height)i + β2(height)2i + i. Y = 253 337 395 451 495 534 573 X = 1 100 10000 1 200 40000 1 300 90000 1 450 202500 1 600 360000 1 800 640000 1 1000 1000000 Then X′Y = 30381711350 1235847500 X′X = 7 3450 23425003450 2342500 1855125000 2342500 1855125000 1590006250000 (X′X)−1 = 1.510 −6.080× 10−3 4.869× 10−6−6.080× 10−3 3.010× 10−5 −2.616× 10−8 4.869× 10−3 −2.616× 10−8 2.397× 10−11 β̂ = (X′X)−1X′Y = 199.910.708 −0.000343 Homework 3 Solution 2 Ting-Li Lin