Lesson plan
Multiple linear regression
Multiple linear regression, also known as multivariable linear regression, is a generalization of simple linear regression to the case of more than one independent variable. The basic model for multiple linear regression is : Y_i = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \ldots + \beta_p X_{ip} + \epsilon_i for each observation i = 1, \ldots , n . In the formula above we consider n observations of one dependent variable and p independent variables. Thus, Y i is the i th observation of the dependent variable, X ij is i th observation of the j th independent variable, j = 1, 2, ..., p. The values β j represent parameters to be estimated, and ε i is the i th independent identically distributed normal error. Nearly all real-world regression models involve multiple predictors, and basic descriptions of linear regression are often phrased in terms of the multiple regression model. Note, however, that in these cases the response variable y is still a scalar. Multiple linear regression is a special case, restricted to one dependent variable, of general linear models (also known as multivariate linear regression), which predicts multiple correlated dependent variables.
Article summary
Multiple linear regression, also known as multivariable linear regression, is a generalization of simple linear regression to the case of more than one independent variable. The basic model for multiple linear regression is : Y_i = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \ldots + \beta_p X_{ip} + \epsilon_i for each observation i = 1, \ldots , n . In the formula above we consider n observations of one dependent variable and p independent variables. Thus, Y i is the i th observation of the dependent variable, X ij is i th observation of the j th independent variable, j = 1, 2, ..., p. The values β j represent parameters to be estimated, and ε i is the i th independent identically distributed normal error. Nearly all real-world regression models involve multiple predictors, and basic descriptions of linear regression are often phrased in terms of the multiple regression model. Note, however, that in these cases the response variable y is still a scalar. Multiple linear regression is a special case, restricted to one dependent variable, of general linear models (also known as multivariate linear regression), which predicts multiple correlated dependent variables.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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