11+Regression

# Now we apply f test calculate the multiple coecient

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Unformatted text preview: ose we want to model the relationship between the sale price and sales revenue. The data are given in the table 13 A. Zhensykbaev Regression # Sales Volume Sale revenue of sales price yi xi 1 xi2 xi1 − x1 xi2 − x2 ¯ ¯ 1 50 5 30 -14.2 -8.4 2 120 7 30 -12.2 -8.4 3 140 11 33 -8.2 -5.4 4 135 16 34 -3.2 -4.4 5 163 16 33 -3.2 -5.4 6 233 21 36 1.8 -2.4 7 241 27 40 7.8 1.6 8 255 26 45 6.8 6.6 9 286 30 50 10.8 11.6 10 330 33 53 13.8 14.6 yi ˆ yi − y ¯ 77.03 -145.3 91.83 -75.3 126.14 -55.3 164.71 -60.3 163.14 -32.3 204.85 37.7 255.53 45.7 255.98 59.7 293.43 90.7 320.34 134.7 The linear model is yi = β0 + β1 xi1 + β2 xi2 + εi (i = 1 : 10). Calculate the means and variances 1 x1 = ¯ 10 10 1 x2 = ¯ 10 xi1 = 19.2, i=1 1 y= ¯ 10 10 xi2 = 38.4, i=1 10 yi = 195.3, i=1 10 10 2 (yi − yi )2 = 3752, ˆ (yi − y ) = 67964.1, ¯ SSyy = i=1 i=1 10 10 2 SSx1 x1 = (xν 1 − x1 ) = 855.6, ¯ (xν 2 − x2 )2 = 618.4, ¯ SSx2 x2 = ν =1 ν =1 10 SSx1 x2 = (xν 1 − x1 )(xν 2 − x2 ) = 677.2, ¯ ¯ ν =1 10 SSx1 y = 10 (xν 1 − x1 )yν = 7400.4, ¯ SSx2 y = ν =1 (xν 2 − x2 )yν = 5986.8. ¯ ν =1 14 A. Zhensykbaev Regression ˆ Now ﬁnd βi : 618.4 · 7400.4 − 677.2 · 5986.8 ˆ β1 = = 7.4, 855.6 · 618.4 − 677.22 855.6 · 5986.8 − 677.2 · 7400.4 ˆ = 1.57 β2 = 855.6 · 618.4 − 677.22 ˆ ˆ ˆ β0 = y − 19.2β1 − 38.4β2 = −7.07. ¯ and yi = y + 7.4(xi1 − 19.2) + 1.57(xi2 − 38.4) ˆ ¯ (i = 1 : 10). The estimated dependence is y = −7.07 + 7.4x1 + 1.57x2 . Now test the hypothesis H0 = {β1 = 0}. (use α = 0.05). Alternative hypothesis is Ha = {β1 >...
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## This note was uploaded on 02/11/2014 for the course MATH 1390 taught by Professor Christopherstocker during the Spring '13 term at Marquette.

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