Let's use the fuel economy data from class. First, we'll load the data:
auto_mpg_all <- read.csv("https://raw.githubusercontent.com/brianlukoff/sta371g/master/data/auto_mpg_all.csv")
There are two ways to include the Yes/No categorical variable After1975 in the regression. One way is to create our own dummy variable that recodes Yes to 1 and No to 0 (or vice versa), and then run a regression including that dummy variable:
auto_mpg$LateModel <- ifelse(auto_mpg$After1975 == "Yes", 1, 0)
model1 <- lm(MPG ~ HP + LateModel, data=auto_mpg_all)
summary(model1)
We can also let R do the heavy lifting for us; by using After1975 directly in the lm command, R creates a dummy variable behind the scenes:
model2 <- lm(MPG ~ HP + After1975, data=auto_mpg_all)
summary(model2)
Note that the output refers to a new variable called After1975Yes; this is a dummy variable where 1 is Yes and 0 is No.
We can do the same with categorical variables that have 3+ categories. For example, suppose we want to include the Origin variable in the model. Add it to the lm command, and R will automatically create dummy variables for all but one of the categories and add them to the model:
model3 <- lm(MPG ~ HP + Origin, data=auto_mpg_all)
summary(model3)
If we want to test the significance of the Origin variable, we must use an ANOVA table to test a compound null hypothesis that all of the dummy variable coefficients for that particular categorical variable are 0 in the population. To do this, first ensure that your model is defined with the categorical variable of interest (Origin in this case) is at the end of the list of variables, and then run the anova command:
model3 <- lm(MPG ~ HP + Origin, data=auto_mpg_all)
anova(model3)