MATH 226 - 9.19.2007

# MATH 226 - 9.19.2007 - i – y-bar 2 Σ(b b 1 x i – b –...

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MATH 226 – September 19, 2007 Find numerical quantities that describe whether the linear model is good or not o raw variation Σ(y i – y-bar) 2 o variation after fitting the line Σ(y i – ŷ i ) 2 o percent of variation explained by the regression line: R 2 = (Σ(y i – y-bar) 2 - Σ(y i – ŷ i ) 2 )/ Σ(y i – y-bar) 2 Coefficient of determination The sample correlation is defined by o ρ = [Σ((x i – x-bar)(y i – y-bar))]/[sqrt((Σ(y i – y-bar) 2 - Σ(y i – y-bar) 2 )] Fact 1 -1≤ ρ ≤ 1 Fact 2 If y = b 0 + b 1 x then ρ = 1 if b 1 >0 and ρ = -1 if b 1 <0 ρ = [Σ((x i – x-bar)(b 0 + b 1 x i – b 0 – b 1 x-bar))]/[sqrt((Σ(y
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Unformatted text preview: i – y-bar) 2- Σ(b + b 1 x i – b – b 1 x-bar) 2 )] • ρ = [b 1 Σ(x i – x-bar) 2 ]/[sqrt(b 1 2 )* Σ(x i – x-bar) 2 Σ(x i – x-bar) 2 ] = b 1 /|b 1 | Fact 3 • Correlation between slope and equation for rho o CAUTIONS Correlations never prove causal relations A linear regression line should only be used over the range of the x-values HOMEWORK o QUESTION 1 b prove your claim o QUESTION 4 c use the TI-89, copy the graphs, normal values on p.89 of text y-bar y i – ybar y i – ŷ i...
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