**Multiple linear regression **is a method you can use to understand the relationship between several explanatory variables and a response variable.

This tutorial explains how to perform multiple linear regression in Stata.

**Example: Multiple Linear Regression in Stata**

Suppose we want to know if miles per gallon and weight impact the price of a car. To test this, we can perform a multiple linear regression using miles per gallon and weight as the two explanatory variables and price as the response variable.

Perform the following steps in Stata to conduct a multiple linear regression using the dataset called *auto*, which contains data on 74 different cars.

**Step 1: Load the data.**

Load the data by typing the following into the Command box:

use http://www.stata-press.com/data/r13/auto

**Step 2: Get a summary of the data.**

Gain a quick understanding of the data you’re working with by typing the following into the Command box:

summarize

We can see that there are 12 different variables in the dataset, but the only ones we care about are *mpg*, *weight*, and *price*.

We can see the following basic summary statistics about these three variables:

**price | **mean = $6,165, min = $3,291, max $15,906

**mpg | **mean = 21.29, min = 12, max = 41

**weight | **mean = 3,019 pounds, min = 1,760 pounds, max = 4,840 pounds

Type the following into the Command box to perform a multiple linear regression using mpg and weight as explanatory variables and price as a response variable.

regress price mpg weight

Here is how to interpret the most interesting numbers in the output:

**Prob > F: **0.000. This is the p-value for the overall regression. Since this value is less than 0.05, this indicates that the combined explanatory variables of *mpg *and *weight *have a statistically significant relationship with the response variable *price*.

**R-squared:** 0.2934. This is the proportion of the variance in the response variable that can be explained by the explanatory variables. In this example, 29.34% of the variation in price can be explained by mpg and weight.

**Coef (mpg): **-49.512. This tells us the average change in price that is associated with a one unit increase in the mpg, *assuming weight is held constant*. In this example, each one unit increase in mpg is associated with an average decrease of about $49.51 in price, assuming weight is held constant.

For example, suppose cars A and B both weigh 2,000 pounds. If car A gets 20 mpg and car B only gets 19 mpg, we would expect the price of car A to be $49.51 less than the price of car B.

**P>|t| (mpg): **0.567. This is the p-value associated with the test statistic for mpg. Since this value is not less than 0.05, we don’t have evidence to say that mpg has a statistically significant relationship with price.

**Coef (weight): **1.746. This tells us the average change in price that is associated with a one unit increase in weight, *assuming mpg is held constant*. In this example, each one unit increase in weight is associated with an average increase of about $1.74 in price, assuming mpg is held constant.

For example, suppose cars A and B both get 20 mpg. If car A weighs one pound more than car B, then car A is expected to cost $1.74 more.

**P>|t| (weight): **0.008. This is the p-value associated with the test statistic for weight. Since this value is less than 0.05, we have sufficient evidence to say that weight has a statistically significant relationship with price.

**Coef (_cons): **1946.069. This tells us the average price of a car when both mpg and weight are zero. In this example, the average price is $1,946 when both weight and mpg are zero. This doesn’t actually make much sense to interpret since the weight and mpg of a car can’t be zero, but the number 1946.069 is needed to form a regression equation.

**Step 4: Report the results.**

Lastly, we want to report the results of our multiple linear regression. Here is an example of how to do so:

Multiple linear regression was performed to quantify the relationship between the weight and mpg of a car and its price. A sample of 74 cars was used in the analysis.

Results showed that there was a statistically significant relationship between weight and price (t = 2.72, p = .008), but there was not a statistically significant relationship between mpg and price (and mpg (t = -.57, p = 0.567).