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(This article was first published on <strong><a href="http://r-exercises.com/2017/01/15/multiple-regression-part-1/?utm_source=rss&utm_medium=rss&utm_campaign=multiple-regression-part-1"> R-exercises</a></strong>, and kindly contributed to <a rel="nofollow" href="https://www.r-bloggers.com/">R-bloggers)</a> </div>
<p><a target="_blank" rel="nofollow" href="http://r-exercises.com/wp-content/uploads/2017/01/fancy-rgl-1.png?x61433"><img sizes="(max-width: 300px) 100vw, 300px" class="wp-image-3848" src="https://i0.wp.com/r-exercises.com/wp-content/uploads/2017/01/fancy-rgl-1-300x300.png?resize=300%2C300" data-recalc-dims="1"></a>In the exercises below we cover some material on multiple regression in R.</p>
<p>Answers to the exercises are available <a target="_blank" rel="nofollow" href="http://r-exercises.com/2017/01/15/multiple-regression-part-1-solutions/">here</a>.</p>
<p>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.</p>
<p>We will be using the dataset <code>state.x77</code>, which is part of the <code>state</code> datasets available in <code>R</code>. (Additional information about the dataset can be obtained by running <code>help(state.x77)</code>.)</p>
<p><strong>Exercise 1</strong></p>
<p>a. Load the <code>state</code> datasets.<br>
b. Convert the <code>state.x77</code> dataset to a dataframe.<br>
c. Rename the <code>Life Exp</code> variable to <code>Life.Exp</code>, and <code>HS Grad</code> to <code>HS.Grad</code>. (This avoids problems with referring to these variables when specifying a model.)</p>
<p><strong>Exercise 2</strong><br>
Suppose we wanted to enter all the variables in a first-order linear regression model with <code>Life Expectancy</code> as the dependent variable. Fit this model.</p>
<p><strong>Exercise 3</strong></p>
<p>Suppose we wanted to remove the <code>Income</code>, <code>Illiteracy</code>, and <code>Area</code> variables from the model in Exercise 2. Use the <code>update</code> function to fit this model.</p>
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<aside><img src="http://r-exercises.com/2017/01/15/multiple-regression-part-1/?utm_source=rss&utm_medium=rss&utm_campaign=multiple-regression-part-1"></aside>
<div><strong>Learn more</strong> about multiple linear regression in the online course <a target="_blank" rel="nofollow" href="http://r-exercises.com/product/linear-regression-in-r-for-data-scientists/">Linear regression in R for Data Scientists</a>. In this course you will learn how to:
<ul>
<li>Model basic and complex real world problem using linear regression</li>
<li>Understand when models are performing poorly and correct it</li>
<li>Design complex models for hierarchical data</li>
<li>And much more</li>
</ul>
</div>
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<p><strong>Exercise 4</strong><br>
Let’s assume that we have settled on a model that has <code>HS.Grad</code> and <code>Murder</code> as predictors. Fit this model.</p>
<p><strong>Exercise 5</strong><br>
Add an interaction term to the model in Exercise 4 (3 different ways).</p>
<p><strong>Exercise 6</strong><br>
For this and the remaining exercises in this set we will use the model from Exercise 4.</p>
<p>Obtain 95% confidence intervals for the coefficients of the two predictor variables.</p>
<p><strong>Exercise 7</strong><br>
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.</p>
<p><strong>Exercise 8</strong></p>
<p>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.</p>
<p><strong>Exercise 9</strong></p>
<p>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.</p>
<p><strong>Exercise 10</strong></p>
<p>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.</p>
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