Lecture 3: Multiple Regression Model - McCombs School of Business

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Garbage Data ◮ R 2 is 26% !! ◮ As usual, we need a statistical notion of how close is close... ◮ It turns out that if we transform R 2 we can solve this. Define f = R 2 /(p − 1) (1 − R 2 )/(n − p) This is the F-test of overall significance. Under the null hypothesis f is distributed: f ∼ F p−1,n−p 24
The F -test Recall what we are testing: H 0 : β 1 = β 2 = . . . β d = 0 H 1 : at least one β j ≠ 0. Under H 0 , f has F p−1,n−p distribution with p − 1 numerator and n − p denominator degrees of freedom. ◮ The F has decreasing variance as the df’s increase. ◮ Generally, f > 4 is very significant (reject the null). The p-value for this test is ϕ = Pr(F p−1,n−p > f ). 25
Page 1 and 2: DMBA: Statistics Lecture 3: Multipl
Page 3 and 4: The Multiple Regression Model Many
Page 5 and 6: The MLR Model Our interpretation of
Page 7 and 8: The Data and Least Squares The data
Page 9 and 10: The Data and Least Squares Fitted V
Page 11 and 12: Residual Standard Error First off,
Page 13 and 14: Residuals in MLR Consider the resid
Page 15 and 16: Inference for Coefficients As befor
Page 17 and 18: In Excel... -"./0$123$4$multiple 1"
Page 19 and 20: Supervisor Performance Data Suppose
Page 21 and 22: Supervisor Performance Data F-tests
Page 23: F-tests Garbage Data ./$0""$12*03$)
Page 27 and 28: The F-test ((7 6 # 5 5#685 Two
Page 29 and 30: Partial F -test With the total F -t
Page 31 and 32: Partial F -test It turns out that u
Page 33: Glossary and Equations F -tests and

Lecture 3: Multiple Regression Model - McCombs School of Business

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