# Mathcad - UF-ESI-6321-13-01-01 - UF-ESI-6321 UF-ESI-01.xmcd...

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UF-ESI-6321 UF-ESI-6321-13-01-01.xmcd page 1 of 3 13.1.1 The multiple linear regression model y β 0 β 1 x 1 + β 2 x 2 + β 3 x 3 + = is fitted to a data set of n 30 := observations. The total sum of squares is SST 108.9 := and the error sum of squares is SSE 12.4 := (a) What is the coefficient of determination R 2 ? SSR SST SSE - 96.5 = := R SSR SST 0.941 = := R 2 0.886 = Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435

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UF-ESI-6321 UF-ESI-6321-13-01-01.xmcd page 2 of 3 (b) Write out the analysis of variance table. k 3 := MSR SSR k := MSE SSE n k - 1 - := i 1 3 .. := j 1 2 .. := l 2 2 .. := F l MSR MSE := v i k n k - 1 - n 1 - := SS i SSR SSE SST := MS j MSR MSE := p l 1 pF F l v 1 , v 2 , ( ) - := v i 3 26 29 = SS i 96.5 12.4 108.9 = MS j 32.167 0.477 = F l 67.446 = p l 0.000 = Source i "Regression" "Error" "Total" := (c) What is the estimate of the error variance σ 2 ? σ SSE n k - 1 - 0.691 = := σ 2 0.477 = Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899
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