10.2 - Inferenceforregression...

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Inference for regression Analysis of variance for regression -   Bivariate normal distribution
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Simple linear regression model
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Simple linear regression model
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Least squares regression line:
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The regression standard error, s, for n sample data points is calculated from the residuals ( y i ŷ i ): 2 ) ˆ ( 2 2 2 - - = - = n y y n residual s i i
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Testing the hypothesis of no relationship We may look for evidence of a significant relationship between variables x and y in the population from which our data were drawn. For that, we can test the hypothesis that the regression slope β is equal to zero.
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Excel
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represents the total variation in the response variable. It can be decomposed as Total sum of squares = model (regression) SS + error (residual) SS SST = SSM + SSE Total variation = explained variation + unexplained variation R 2 = SSM/SST, also the square of the sample correlation SST = (n -1)(s y ) 2 SSE = (n - 2)s 2
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An alysis o f va riance identity ANOVA
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Reject the hypothesis that β 1 = 0 (no linear relationship) if
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β 1  = 0 (no linear  relationship) if  is large. Model mean square
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10.2 - Inferenceforregression...

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