IPS6eCh10_1

# IPS6eCh10_1 - Inference for Regression Simple Linear...

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Inference for Regression Simple Linear Regression IPS Chapter 10.1 © 2009 W.H. Freeman and Company

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Objectives (IPS Chapter 10.1) Simple linear regression Statistical model for linear regression Estimating the regression parameters Confidence interval for regression parameters Significance test for the slope Confidence interval for µ y Prediction intervals
Statistical model for linear regression

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ŷ unbiased estimate for mean response μ y b 0 unbiased estimate for intercept β 0 b 1 unbiased estimate for slope 1 Estimating the parameters

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The regression standard error, s , for n sample data points is calculated from the residuals ( y i ŷ i ): The population standard deviation σ for y at any given value of x represents the spread of the normal distribution of the ε i around the mean μ y . 2 ) ˆ ( 2 2 2 - - = - = n y y n residual s i i

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Conditions for inference The observations are independent. The relationship is indeed linear. The standard deviation of y, σ , is the same for all values of x . The response y varies normally around its mean.

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Using residual plots to check for regression validity The residuals ( y ŷ ) give useful information about the contribution of individual data points to the overall pattern of scatter.
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IPS6eCh10_1 - Inference for Regression Simple Linear...

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