Linear regression is a method we can use to understand the relationship between one or more explanatory variables and a response variable.

When we perform linear regression on a dataset, we end up with a regression equation which can be used to predict the values of a response variable, given the values for the explanatory variables.

We can then measure the difference between the predicted values and the actual values to come up with the **residuals** for each prediction. This helps us get an idea of how well our regression model is able to predict the response values.

This tutorial explains how to obtain both the **predicted values **and the **residuals **for a regression model in Stata.

**Example: How to Obtain Predicted Values and Residuals**

For this example we will use the built-in Stata dataset called *auto*. We’ll use *mpg *and *displacement *as the explanatory variables and *price *as the response variable.

Use the following steps to perform linear regression and subsequently obtain the predicted values and residuals for the regression model.

**Step 1: Load and view the data.**

First, we’ll load the data using the following command:

sysuse auto

Next, we’ll get a quick summary of the data using the following command:

summarize

**Step 2: Fit the regression model.**

Next, we’ll use the following command to fit the regression model:

regress price mpg displacement

The estimated regression equation is as follows:

estimated price = 6672.766 -121.1833*(mpg) + 10.50885*(displacement)

**Step 3: Obtain the predicted values.**

We can obtain the predicted values by using the **predict **command and storing these values in a variable named whatever we’d like. In this case, we’ll use the name **pred_price**:

predict pred_price

We can view the actual prices and the predicted prices side-by-side using the **list **command. There are 74 total predicted values, but we’ll view just the first 10 by using the **in 1/10 **command:

list price pred_price in 1/10

**Step 4: Obtain the residuals.**

We can obtain the residuals of each prediction by using the **residuals **command and storing these values in a variable named whatever we’d like. In this case, we’ll use the name **resid_price**:

predict resid_price, residuals

We can view the actual price, the predicted price, and the residuals all side-by-side using the **list **command again:

list price pred_price resid_price in 1/10

**Step 5: Create a predicted values vs. residuals plot.**

Lastly, we can created a scatterplot to visualize the relationship between the predicted values and the residuals:

scatter resid_price pred_price

We can see that, on average, the residuals tend to grow larger as the fitted values grow larger. This could be a sign of heteroscedasticity – when the spread of the residuals is not constant at every response level.

We could formally test for heteroscedasticity using the Breusch-Pagan Test and we could address this problem using robust standard errors.

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