Want to share your content on R-bloggers? click here if you have a blog, or here if you don't. In the exercises below we cover some material on multiple regression in R.

Answers to the exercises are available here.

If you obtained a different (correct) answer than those listed on the solutions page, please feel free to post your answer as a comment on that page.

We will be using the dataset `state.x77`, which is part of the `state` datasets available in `R`. (Additional information about the dataset can be obtained by running `help(state.x77)`.)

Exercise 1

a. Load the `state` datasets.
b. Convert the `state.x77` dataset to a dataframe.
c. Rename the `Life Exp` variable to `Life.Exp`, and `HS Grad` to `HS.Grad`. (This avoids problems with referring to these variables when specifying a model.)

Exercise 2
Suppose we wanted to enter all the variables in a first-order linear regression model with `Life Expectancy` as the dependent variable. Fit this model.

Exercise 3

Suppose we wanted to remove the `Income`, `Illiteracy`, and `Area` variables from the model in Exercise 2. Use the `update` function to fit this model.

Learn more about multiple linear regression in the online course Linear regression in R for Data Scientists. In this course you will learn how to:

• Model basic and complex real world problem using linear regression
• Understand when models are performing poorly and correct it
• Design complex models for hierarchical data
• And much more

Exercise 4
Let’s assume that we have settled on a model that has `HS.Grad` and `Murder` as predictors. Fit this model.

Exercise 5
Add an interaction term to the model in Exercise 4 (3 different ways).

Exercise 6
For this and the remaining exercises in this set we will use the model from Exercise 4.

Obtain 95% confidence intervals for the coefficients of the two predictor variables.

Exercise 7
Predict the Life Expectancy for a state where 55% of the population are High School graduates, and the murder rate is 8 per 100,000.

Exercise 8

Obtain a 98% confidence interval for the mean Life Expectancy in a state where 55% of the population are High School graduates, and the murder rate is 8 per 100,000.

Exercise 9

Obtain a 98% confidence interval for the Life Expectancy of a person living in a state where 55% of the population are High School graduates, and the murder rate is 8 per 100,000.

Exercise 10

Since our model only has two predictor variables, we can generate a 3D plot of our data and the fitted regression plane. Create this plot.