multiregress2 - Multiple Regression II F-test for overall...

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Multiple Regression II Using the Estimated Regression Equation for Estimation and Prediction F-test for overall significance Qualitative Independent Variables
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Testing for Significance: F Test Hypotheses Rejection Rule Test Statistics H 0 : 1 = 2 = . . . = p = 0 H a : One or more of the parameters is not equal to zero. F = MS(model)/MS(error) Reject H 0 if p -value < a or if F > F a , where F is based on an F distribution with p d.f. in the numerator and n - p - 1 d.f. in the denominator. What happens when H 0 is true? What is the range for F statistics in the case of multiple linear regression?
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F Test for Overall Significance Hypotheses H 0 : 1 = 2 = 0 H a : One or both of the parameters is not equal to zero. Rejection Rule For a = .05 and d.f. = 2, 17; F .05 = 3.59 Reject H 0 if p -value < .05 or F > 3.59
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Excel’s ANOVA Output A B C D E F 32 33 34 df SS MS F Significance F 35 Regression 2 500.3285 250.1643 42.76013 2.32774E-07 36 Residual 17 99.45697 5.85041 37 Total 19 599.7855 38 F Test for Overall Significance p -value used to test for overall significance
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F Test for Overall Significance Test Statistics F = MSR/MSE = 250.16/5.85 = 42.76 Conclusion p -value < .05, so we can reject H 0 . (Also, F = 42.76 > 3.59)
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General guideline for checking the utility of a multiple regression model Conduct a test of overall model adequacy using F-test Conduct t-tests only on those β parameters you are particularly interested in. However, it is important to limit the number of tests being performed.
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This note was uploaded on 09/28/2011 for the course STAT METHO 33:623:385 taught by Professor Faridalizadeh during the Spring '11 term at Rutgers.

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multiregress2 - Multiple Regression II F-test for overall...

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