Multiple Linear Regression

Learn how to build and interpret linear regression models with more than one predictor.

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Key Concepts

Review core concepts you need to learn to master this subject

Multiple Regression Coefficient

Multiple Regression in Python

Binary Predictors in Multiple Regression

Multiple Linear Regression Interpretation

Visualizing a Multiple Regression Model

Coefficients in Multiple Regression

Multicollinearity Assumption

Multiple Linear Regression

Multiple linear regression is an extension of simple linear regression used to model the relationship between a quantitative response variable and two or more predictors, which may be quantitative, categorical, or a mix of both. This allows us to control for confounding variables, which may distort the perceived relationship between two variables if not accounted for.

Multiple Linear Regression

Lesson 1 of 2

1
Introduction to Multiple Regression
Simple linear regression may be used to understand and make predictions about the relationship between two variables. But what happens when there are more than two variables? When we want to u…
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2
Multiple Regression Model Equation
We often write the equation of a line in the form y=mx+b, where m is the slope of the line and b is the y-intercept. Since we will be adding at least two predictors to a multiple regression…
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3
Fitting a Multiple Regression in Python
To run a multiple linear regression in Python, we can use the function OLS.from_formula() from statsmodels.api. For example, if we want to run a regression to predict score using hours_studied and …
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4
Binary Categorical Variables in Multiple Regression
Binary categorical variables are variables with exactly two possible values. In a regression model, these two values are generally coded as 1 or 0. For example, a multiple regression equation from …
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5
Interpretation of Binary Categorical Variables
While we can view a binary categorical variable as a way of creating two new regression equations with different intercepts, we don’t need to make these equations every time we want to interpret a …
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6
Quantitative Variables in Multiple Regression
In the previous exercises, we looked at regression models with one quantitative predictor and one binary predictor, but we can also have models with multiple quantitative predictors. For example, c…
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7
Interpretation of Quantitative Variables
In a multiple regression model, the coefficient on a quantitative predictor is the expected difference in the outcome variable for a one-unit increase of the predictor, holding all other predictors…
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8
Changes in Predictor Coefficients
Sometimes we use regression to understand the relationship between two variables because we wish to control for potential confounders. For example, based on the survey dataset, we may be primarily …
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9
Simpson's Paradox
In the last exercise, we explored how a coefficient may change when additional predictors are added to a model. When adding predictors entirely reverses the sign of the coefficient, this is called …
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10
Assumptions of Multiple Regression
When doing any type of statistical analysis, we should always keep the assumptions in mind. Multiple linear regression requires some of the same assumptions as simple linear regression: 1. Linea…
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11
Review
Congratulations! In this lesson you’ve learned to: * Fit a multiple linear regression model in Python * Write and interpret a multiple regression model * Understand what binary and quantitati…
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