> drop1(fuel.fit) Single term deletions Model: 100/Mileage ~ Weight + Disp. Df Sum of Sq RSS CpConversely, one may want to see the effect of adding one term from each of a possible choice of terms.
8.67331 9.58629 Weight 1 7.931031 16.60434 17.21299 Disp. 1 0.044814 8.71812 9.32678
> fit0_lm(100/Mileage~1, car.test.frame) * model fitting only the intercept * investigate one-variable fits by adding each term to the model > add1(fit0, .~ Weight + Disp. + Type) Single term additions Model: 100/Mileage ~ 1 Df Sum of Sq RSS CpIn both cases, the order of the terms in the model formula is unimportant since the effect of each term on the initial model is evaluated separately. For stepwise selection of models, the function step() can be used:
33.85687 35.00456 Weight 1 25.13875 8.71812 11.01350 Disp. 1 17.25253 16.60434 18.89972 Type 5 24.23960 9.61727 16.50341
>fuel.step_step(fit0, .~Weight + Disp. + Type, trace=F, direction="both")
> fuel.step Call: lm(formula = 100/Mileage ~ Weight, data = car.test.frame) Coefficients: (Intercept) Weight 0.3914324 0.00131638 Degrees of freedom: 60 total; 58 residual Residual standard error (on weighted scale): 0.3877015By default, the trace argument =TRUE. In this case, information is printed while step() is running. Other arguments allow the user to specify the stopping criteria or the range of the models examined in the stepwise search.
The anova() function works in two ways: given a single object, anova() fits a sequence of models by successively adding each of the terms to the model (from last to first). Given more than one fitted model as arguments, anova() makes sequential pairwise comparisons in the order the fitted models are listed.
Analysis of Variance Table Response: 100/Mileage Terms added sequentially (first to last) Df Sum of Sq Mean Sq F Value Pr(F) Weight 1 25.13875 25.13875 165.2090 0.0000000 Disp. 1 0.04481 0.04481 0.2945 0.5894582 Residuals 57 8.67331 0.15216Notice the difference between anova() and add1(). Here the terms are added to the model sequentially whereas using the add1() function, each term is added seperately to the original model.
> fuel.fit2_lm(update(fuel.fit, . ~ . + Type))
> anova(fuel.fit, fuel.fit2)
Analysis of Variance Table Response: 100/Mileage Terms Resid. Df RSS Test Df Sum of Sq F Value 1 Weight + Disp. 57 8.673309 2 Weight + Disp. + Type 52 5.124531 +Type 5 3.548778 7.202082 Pr(F) 1 2 3.465263e-05
Analysis of Variance