Eliminating variables from the model - adjusted R-squared selection

Now you will create a new model, where you will drop the variable that when dropped yields the highest improvement in the adjusted $R^2$.

This exercise is part of the course

Data Analysis and Statistical Inference

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Exercise instructions

Create a new model, m1, where you remove rank from the list of explanatory variables. Check out the adjusted $R^2$ of this new model and compare it to the adjusted $R^2$ of the full model.
If you don't want to view the entire model output, but just the adjusted R-squared, use summary(m1)$adj.r.squared.
Create another new model, m2, where you remove ethnicity from the list of explanatory variables. Check out the adjusted $R^2$ of this new model and compare it to the adjusted $R^2$ of the full model.
Repeat until you have tried removing each variable from the full model m_full at a time, and determine the removal of which variable yields the highest improvement in the adjusted $R^2$.
Make note of this variable (you will be asked about it in the next question).

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# The evals data frame is already loaded into the workspace

# The full model:
m_full <- lm(score ~ rank + ethnicity + gender + language + age + cls_perc_eval + cls_students +
               cls_level + cls_profs + cls_credits + bty_avg, data = evals)
summary(m_full)$adj.r.squared

# Remove rank:
m1 <- lm(score ~ ethnicity + gender + language + age + cls_perc_eval + cls_students + cls_level +
           cls_profs + cls_credits + bty_avg, data = evals)
summary(m1)$adj.r.squared

# Remove ethnicity:
m2 <-
summary(m2)$adj.r.squared

# Remove gender:
m3 <-
summary(m3)$adj.r.squared

# ...

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