<p>Beyond the assumption of multi-collinearity pointed out by @Mike J,  the economist's goal is to infer that one variable (such as education) has a causal effect on 
another variable (such as wages). This is known as the notion of <strong>ceteris paribus</strong>, which means <em>holding other relevant factors constant</em>.  </p>

<h2>Multiple regression analysis is more amenable to ceteris paribus analysis</h2>

<p>It allows us to explicitly control for many other factors that simultaneously affect the dependent variable. This explains why your coefficient on <code>years of education</code> in a simple regression is different from the one you get when you regress wages on <code>years of education</code> and <code>test scores</code>. In the multiple regression case you control for test scores, so the effect of education will be conditional on test scores. In other words, you are taking `test scores' out of the error term and put it explicitly into the equation. </p>

<h2>Two important notes</h2>

<ol>
<li>The interpretation of the <code>years of education</code> estimate is now
different.  You are comparing the effect of an additional year of
education for a <em>given test score</em>. For example, in the case of a
simple regression, you compare Jane, who had 12 years of education
and a score of 90, to John, who had 11 years of education and a
score of 50. In the case of a multiple regression, you would compare
a Jane and a John with the <strong><em>same test score</em></strong> but with a
difference of one year of education.</li>
<li>Economists do not believe that multiple regression analysis buys you
causality, but it is at least better than simple regression!</li>
</ol>

CC BY-SA 4.0
2020-04-08T01:42:06.483Z
This is an awesome explanation, makes a lot more sense now. Appreciate it!
Yash
CC BY-SA 4.0
2020-04-06T16:50:49.813Z
2020-04-06T20:34:57.943Z
2020-04-06T20:34:57.943Z
emeryville
<p>The data might be correlated which can lead to simple and multiple linear regression models giving different results. </p>

<p>Which goes against the assumption of no multi-collinearity:
Multicollinearity occurs when independent variables in a regression model are correlated.</p>

<p>When modeling <code>years of education</code> to <code>wages</code>, the results may show significance but modeling both <code>years of education</code> and <code>test scores</code> could show <code>years of education</code> as not significant because <code>years of education</code> and <code>test scores</code> are correlated. </p>

<p>Try  plotting <code>years of education</code> and <code>test scores</code>.</p>

CC BY-SA 4.0
2020-04-06T02:21:20.330Z
2020-04-06T16:25:37.490Z
2020-04-06T16:25:37.490Z
Mike J
<p>Context: I'm an undergrad who took Intermediate Econometrics more than a year ago and I'm trying to brush up on some of the skills.</p>

<p>As I was reviewing multiple regression, I realized I didn't quite understand what makes the regressor coefficients different when doing a multiple regression vs doing a univariate regression. For instance, if I were to regress <code>wages</code> on <code>years of education</code>, why would the coefficient on <code>years of education</code> be different than when I regressed wages on <code>years of education</code> and <code>test scores</code>?</p>

<econometrics><regression>
Difference between a multiple regression and several linear regressions?
Yash
# Difference between a multiple regression and several linear regressions?

(Asked by: username_0 on 2020-04-05)

Context: I'm an undergrad who took Intermediate Econometrics more than a year ago and I'm trying to brush up on some of the skills.

As I was reviewing multiple regression, I realized I didn't quite understand what makes the regressor coefficients different when doing a multiple regression vs doing a univariate regression. For instance, if I were to regress `wages` on `years of education`, why would the coefficient on `years of education` be different than when I regressed wages on `years of education` and `test scores`?

**Tags:** econometrics, regression

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## 2 answers

### Answer by username_1 on 2020-04-06. Score: 0 | Accepted answer

Beyond the assumption of multi-collinearity pointed out by @Mike J, the economist's goal is to infer that one variable (such as education) has a causal effect on
another variable (such as wages). This is known as the notion of **ceteris paribus**, which means *holding other relevant factors constant*.

## Multiple regression analysis is more amenable to ceteris paribus analysis

It allows us to explicitly control for many other factors that simultaneously affect the dependent variable. This explains why your coefficient on `years of education` in a simple regression is different from the one you get when you regress wages on `years of education` and `test scores`. In the multiple regression case you control for test scores, so the effect of education will be conditional on test scores. In other words, you are taking `test scores' out of the error term and put it explicitly into the equation.

## Two important notes

1. The interpretation of the `years of education` estimate is now
   different. You are comparing the effect of an additional year of
   education for a *given test score*. For example, in the case of a
   simple regression, you compare Jane, who had 12 years of education
   and a score of 90, to John, who had 11 years of education and a
   score of 50. In the case of a multiple regression, you would compare
   a Jane and a John with the ***same test score*** but with a
   difference of one year of education.
2. Economists do not believe that multiple regression analysis buys you
   causality, but it is at least better than simple regression!

> **Comments:**
> **username_0**: This is an awesome explanation, makes a lot more sense now. Appreciate it!  

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### Answer by username_2 on 2020-04-06. Score: 1

The data might be correlated which can lead to simple and multiple linear regression models giving different results.

Which goes against the assumption of no multi-collinearity:
Multicollinearity occurs when independent variables in a regression model are correlated.

When modeling `years of education` to `wages`, the results may show significance but modeling both `years of education` and `test scores` could show `years of education` as not significant because `years of education` and `test scores` are correlated.

Try plotting `years of education` and `test scores`.


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