What is Multiple Linear Regression?
Multiple linear regression is the most common form of linear regression analysis. Multiple linear regression uses predictive analysis to explain the relationship between one continuous dependent variable and two or more independent variables. The independent variables can be continuous or categorical (dummy coded as appropriate).
Example Questions Answered:
Do age and IQ scores effectively predict GPA?
Do weight, height, and age explain the variance in cholesterol levels?
Assumptions:
Additionally, regression residuals must follow a normal distribution.
Furthermore, we assume a linear relationship between the dependent variable and the independent variables.
The residuals are homoscedastic and approximately rectangular-shaped.
The model assumes no multicollinearity, meaning the independent variables do not have high correlations.
At the center of the multiple linear regression analysis is the task of fitting a single line through a scatter plot. More specifically the multiple linear regression fits a line through a multi-dimensional space of data points. The simplest form has one dependent and two independent variables. We may also refer to the dependent variable as the outcome variable or regression. We may also refer to the independent variables as the predictor variables or regressors.
When selecting the model for multiple linear regression analysis, we must also consider the model fit.
Second, it forecasts the effects of changes, showing how much the dependent variable changes with adjustments in the independent variables. For example, it shows how much GPA changes with each one-point change in IQ.
Third, it predicts trends and future values. It provides point estimates. An example question may be “what will the price of gold be 6 month from now?”
When selecting a model for it, we must consider model fit. Adding independent variables always increases the explained variance (R²) in the dependent variable. However, adding too many variables without theoretical justification can lead to an over-fit model.
Related Pages:
Conduct and Interpret a Multiple Linear Regression
Assumptions of Multiple Linear Regression
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