11+Regression

Now we apply f test calculate the multiple coecient

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 >...
View Full Document

This note was uploaded on 02/11/2014 for the course MATH 1390 taught by Professor Christopherstocker during the Spring '13 term at Marquette.

Ask a homework question - tutors are online