# problem-11.26

problem-11.26 This can be carried out as follows:

    > with(grip, interaction.plot(grip.type,person,UBP))
    > res.int = lm(UBP ~ person * grip.type, data=grip)
    > res.noint = lm(UBP ~ person + grip.type, data=grip)
    > res.per = lm(UBP ~ person, data=grip)
    > res.grip = lm(UBP ~ grip.type, data=grip)
    > res.none = lm(UBP ~ 1, data=grip)

Now, we check to see what is statistically significant:

    > anova(res.noint,res.int)
    Analysis of Variance Table

    Model 1: UBP ~ person + grip.type
    Model 2: UBP ~ person * grip.type
      Res.Df RSS Df Sum of Sq    F Pr(>F)
    1     30 509
    2     24 484  6        25 0.21   0.97

This agrees with the interaction plot. No evidence of an interaction is present.

    > anova(res.none,res.per)
    Analysis of Variance Table

    Model 1: UBP ~ 1
    Model 2: UBP ~ person
      Res.Df RSS Df Sum of Sq    F Pr(>F)
    1     35 876
    2     32 848  3        27 0.34    0.8

No evidence that the difference varies among subjects (recall that this is simulated data).

    > anova(res.none,res.grip)
    Analysis of Variance Table

    Model 1: UBP ~ 1
    Model 2: UBP ~ grip.type
      Res.Df RSS Df Sum of Sq    F  Pr(>F)
    1     35 876
    2     33 536  2       339 10.4 0.00031 ***
    ---
    Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

The effect of the grip seems significant.
Finally, we see that stepAIC() returns the same conclusion.

    > library(MASS)
    > stepAIC(res.int)
    ...
    Call:
    lm(formula = UBP ~ grip.type, data = grip)
    ...