- Write and describe a multiple linear regression model equation
- Calculate and describe the unadjusted coefficient of determination
- Assess the model assumptions with a residual or a predicted values plot
Multiple Linear Regression
Multiple Linear Regression
Multiple linear regression is a statistical modeling technique used to understand the relationship between a dependent variable and two or more independent variables.
It extends the concept of simple linear regression, which examines the relationship between a dependent variable and a single independent variable, therefore, it is called “simple”.
In multiple linear regression, the goal is to create a linear equation that best fits the data and can be used to predict the value of the dependent variable based on the values of multiple independent variables.
Multiple Linear Regression Equation
The equation takes the form:
[latex]y = β_0 + β_1 x_1 + β_2 x_2 + ... + β_p x_p[/latex]
where:
- [latex]y[/latex] is the dependent variable (the variable to be predicted or explained)
- [latex]x_1, x_2, ..., x_p[/latex] are the independent variables (also known as predictor variables or features)
- [latex]β_0, β_1, β_2, ..., β_p[/latex] are the regression coefficients (the estimated coefficients that represent the relationship between each independent variable and the dependent variable.
The multiple linear regression model estimates the regression coefficients ([latex]β_0, β_1, β_2, ..., β_p[/latex]) that minimize the sum of squared residuals (the difference between the predicted values and the actual values of the dependent variable). The coefficients provide information about the magnitude and direction of the relationship between each independent variable and the dependent variable, while taking into account the influence of other independent variables in the model.
Multiple linear regression analysis is widely used in various fields, including social sciences, economics, finance, and data analysis, to understand and predict the relationship between multiple variables. It allows for the examination of complex relationships and provides insights into how changes in one or more independent variables impact the dependent variable.