The Boston data set contains 13 variables, and so it would be cumbersome
to have to type all of these in order to perform a regression using all of the
predictors.
Instead, we can use the .
(dot) as short-hand:
lm(formula = medv ~ ., data = Boston)
The dot wil resolve to all variables in the dataset except the one that is given as dependent variable.
> summary(lm.fit) Call: lm(formula = medv ~ ., data = Boston) Residuals: Min 1Q Median 3Q Max -15.595 -2.730 -0.518 1.777 26.199 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3.646e+01 5.103e+00 7.144 3.28e-12 *** crim -1.080e-01 3.286e-02 -3.287 0.001087 ** zn 4.642e-02 1.373e-02 3.382 0.000778 *** indus 2.056e-02 6.150e-02 0.334 0.738288 chas 2.687e+00 8.616e-01 3.118 0.001925 ** nox -1.777e+01 3.820e+00 -4.651 4.25e-06 *** rm 3.810e+00 4.179e-01 9.116 < 2e-16 *** age 6.922e-04 1.321e-02 0.052 0.958229 dis -1.476e+00 1.995e-01 -7.398 6.01e-13 *** rad 3.060e-01 6.635e-02 4.613 5.07e-06 *** tax -1.233e-02 3.760e-03 -3.280 0.001112 ** ptratio -9.527e-01 1.308e-01 -7.283 1.31e-12 *** black 9.312e-03 2.686e-03 3.467 0.000573 *** lstat -5.248e-01 5.072e-02 -10.347 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 4.745 on 492 degrees of freedom Multiple R-squared: 0.7406, Adjusted R-squared: 0.7338 F-statistic: 108.1 on 13 and 492 DF, p-value: < 2.2e-16
We can access the individual components of a summary object by name
(type ?summary.lm
to see what is available). Hence summary(lm.fit)$r.sq
gives us the summary(lm.fit)$sigma
gives us the RSE.
Try receiving the
Assume that:
MASS
library has been loadedBoston
dataset has been loaded and attached