lm Function in R

Many generic functions are available for the computation of regression coefficients, for example, testing the coefficients, computing the residuals, prediction values, etc. Therefore, a good grasp of the lm() function is necessary. Suppose, we have performed the regression analysis using the lm function as done in the previous lesson.

mod <- lm(mpg ~ hp, data = mtcars)

Objects of “lm” Class

The object returned by the lm() function has a class of “lm”. The objects associated with the “lm” class have mode as a list.

class(mod)

The name of the objects related to the “lm” class can be queried via

names(mod)

All the components of the “lm” class can be assessed directly. For example,

mod$rank

mod$coef   # or mod$coefficients

Generic Functions of “lm” model

The following is the list of some generic functions for the fitted “lm” model.

Generic FunctionShort Description
print()print or display the results in the R Console
summary()print or displays regression coefficients, their standard errors, t-ratios, p-values, and significance
coef()extracts regression coefficients
residuals()or resid(): extracts residuals of the fitted model
fitted()or fitted.values() : extracts fitted values
anova()perform comparisons of the nested model
predict()compute predicted values for new data
plot()draw a diagnostics plot of the regression model
confint()compute the confidence intervals for regression coefficients
deviance()compute the residual sum of squares
vcov()compute estimated variance-covariance matrix
logLik()compute the log-likelihood
AIC(), BIC()compute information criteria

It is better to save objects from the summary() function.

The summary() function returns an object of class “summy.lm()” and its components can be queried via

sum_mod <- summary(mod)

names(sum_mod)
names( summary(mod) )
lm class objects

The objects from the summary() function can be obtained as

sum_mod$residuals
sum_mod$r.squared
sum_mod$adj.r.squared
sum_mod$df
sum_mod$sigma
sum_mod$fstatistic

Computation and Visualization of Prediction and Confidence Interval

The confidence interval for estimated coefficients can be computed as

confint(mod, level = 0.95)

Note that level argument is optional if the confidence level is 95% (significance level is 5%).

The prediction intervals for mean and individual for hp (regressor) equal to 200 and 160, can be computed as

predict(mod, newdata=data.frame(hp = c(200, 160)), interval = "confidence" )
predict(mod, newdata=data.frame(hp = c(200, 160)), interval = "prediction" )

The prediction intervals can be used for computing and visualizing confidence bands. For example,

x = seq(50, 350, length = 32 )
pred <- predict(mod, newdata=data.frame(x), interval = "prediction" )

plot(hp, mpg)
lines(pred[,1] ~ x, col = 1) # fitted values
lines(pred[,2] ~ x, col = 2) # lower limit
lines(pred[,3] ~ x, col = 2) # upper limit
Visualization of prediction intervals and confidence band

For diagnostics plot, the plot() function can be used and it provides four graphs of

  • residuals vs fitted values
  • QQ plot of standardized residuals
  • scale-location plot of fitted values against the square root of standardized residuals
  • standardized residuals vs leverage
diagnostic plot of model from lm function

To plot say QQ plot only use

plot(mod, which = 2)

which argument is used to select the graph produced out of four.

Test Preparation MCQs

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