Updating Models

The simplest way to remove urban70 would be to create a new model which does not include it. However, retyping the formulae can get tiresome, especially when a lot of terms are involved. A fancier way to change the model is with the update function.

> education.lm <- update(education.lm, . ~ . - Urban70)

This assigns a new value to education.lm. The new value is education.lm, updated to have the same response (the . before the ~ means the same thing is being predicted) and using the same predictors, except without Urban70. The new model looks like this:

> summary(education.lm)

Call: lm(formula = SE70 ~ PI68 + Y69)
Residuals:
    Min     1Q Median    3Q   Max
 -51.42 -18.17 -1.768 15.32 53.16

Coefficients:
                Value Std. Error   t value  Pr(>|t|)
(Intercept) -301.0892   70.2713    -4.2847    0.0001
       PI68    0.0612    0.0074     8.2532    0.0000
        Y69    0.8361    0.1733     4.8253    0.0000

Residual standard error: 28.97 on 48 degrees of freedom
Multiple R-Squared: 0.6267
F-statistic: 40.3 on 2 and 48 degrees of freedom, the p-value is 5.354e-11

Correlation of Coefficients:
     (Intercept)    PI68
PI68 -0.4839
 Y69 -0.9402      0.1624

Let's check for an interaction between the two significant terms. Note that when you enter an interaction, the main effects are included as well.

> education.lm <- update(education.lm, . ~ PI68*Y69)
> summary(education.lm)

Call: lm(formula = SE70 ~ PI68 + Y69 + PI68:Y69)
Residuals:
    Min     1Q Median    3Q   Max
 -44.55 -17.02 -1.733 13.56 52.48

Coefficients:
                Value Std. Error   t value  Pr(>|t|)
(Intercept)  245.8215  328.7258     0.7478    0.4583
       PI68   -0.1017    0.0960    -1.0592    0.2949
        Y69   -0.6669    0.8995    -0.7414    0.4621
   PI68:Y69    0.0004    0.0003     1.7016    0.0954

Residual standard error: 28.41 on 47 degrees of freedom
Multiple R-Squared: 0.6484
F-statistic: 28.89 on 3 and 47 degrees of freedom, the p-value is 9.728e-11

Correlation of Coefficients:
         (Intercept)    PI68     Y69
    PI68 -0.9826
     Y69 -0.9974      0.9815
PI68:Y69  0.9778     -0.9971 -0.9820

The interaction term really messed up the model, so we should go back to the previous model by removing it.

> education.lm <- update(education.lm, . ~ . - PI68:Y69)

The PI68:Y69 term means ``the PI68 and Y69 interaction'', so if we subtract PI68:Y69 we are left with the main effects only.