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IPS6eCh10_2

# IPS6eCh10_2 - Inference for Regression More Detail about...

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Inference for Regression More Detail about Simple Linear Regression IPS Chapter 10.2 © 2009 W.H. Freeman and Company

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Objectives (IPS Chapter 10.2) Inference for regression—more details Analysis of variance for regression Calculations for regression inference Inference for correlation We will NOT cover the ANOVA F test
Analysis of variance for regression The regression model is: Data = fit + residual y i = ( β 0 + β 1 x i ) + ( ε i )

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Coefficient of determination,  r The coefficient of determination, r 2 , square of the correlation coefficient, is the percentage of the variance in y (vertical scatter from the regression line) that can be explained by changes in x . SST SSM ) ( ) ˆ ( 2 2 2 = - - = y y y y r i i r 2 = variation in y caused by x (i.e., the regression line) total variation in observed y values around the mean

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To estimate or predict responses, we calculate the following standard errors (these will be provided on the final exam, if needed).

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IPS6eCh10_2 - Inference for Regression More Detail about...

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