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Lecture26

# Lecture26 - Review Multiple Linear Regression Inferential...

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4/20/2011 1 Inferential Methods in Regression and Correlation Chapter 11 Review Multiple Linear Regression Model Utility Test: What is the null hypothesis? What is the alternative hypothesis? What is the test statistic? Model Utility Test H0: β1=β2=β3= … =βk =0 Ha: at least one among β1, β2, …, βk is not 0 Test statistic: Today: Learn F distribution and pvalue lookup F MS Re gr MS Re sid MSM MSE Model Utility Test for example 11.12 Model Utility Test H0: β1=β2=β3= … =βk =0 (no useful model) Ha: at least one among β1, β2, …, βk is not 0 Test statistic: From SAS output, pvalue<0.001. Reject H0 Conclusion: There is a useful linear relationship between y and at least one of the four predictors in the model. F MS Re gr MS Re sid MSM MSE 15.60 Density curve of an F distribution P-value F statistic

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4/20/2011 2 The F distribution Family identified by two degrees of freedom: Numerator or Regression Model df1 = k Denominator or Error df2 = n k 1 The df add up: It is strongly right skewed and always positive. Table VIII (pages 573 - 576) Total Regression Model Residual (Error) df n-1 = k n-k-1 F MS Re gr MS Re sid MSM MSE 15.60 How to use the F Table F Critical Values Find the F critical value based on df1 = 5 and df2=8 that captures an upper-tail area of 0.05 F* = 3.69 This means P(F>3.69) = 0.05 Example In a MLR model utility test H0: β
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Lecture26 - Review Multiple Linear Regression Inferential...

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