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Unformatted text preview: ales and females. Do these plots suggest the possible need for the interaction
terms between sex and the other predictors?
(b) Fit a model with gamble as the response and the other variables as predictors that includes the interaction terms between sex and the other predictors. Determine whether
this model may be reasonably simpliﬁed. Exercise 3
Suppose a complete secondorder model
yi = b0 + b1 xi1 + b2 xi2 + b3 xi1 xi2 + b4 x21 + b5 x22 + ei
i
i
was ﬁt to n = 24 observations.
> sum( lm( y ~ 1 )$residuals^2 )
[1] 360
> sum( lm(y ~ x1+x2)$residuals^2 )
[1] 126
> sum( lm(y ~ x1+x2+I(x1*x2))$residuals^2 )
[1] 100
> sum( lm(y ~ x1+x2+I(x1*x2)+I(x1^2)+I(x2^2))$residuals^2 )
[1] 72
(a) Perform the “signiﬁcance of the regression” test at a 5% level of signiﬁcance.
(b) Test whether the secondorder terms are signiﬁcant at a 5% leve...
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 Spring '08
 Stepanov
 Statistics

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