# Multiple Linear Regression

One purpose of linear regression is to
predict a dependent variable based on the value of one or more independent
variables. A linear regression model with only one independent variable is
called simple linear regression.

However, most real world phenomena are multi-factorial in nature, meaning there is more than one factor that impacts on, or causes changes in the dependent variable. In order to predict the dependent variable as accurately as possible, it is usually necessary to include multiple independent variables in the model. Multiple linear regression allows us to test how well we can predict a dependent variable on the basis of multiple independent variables.

### Multiple Linear Regression Example

Suppose you have a data set consisting of the gender, height and age of children between 5 and 10 years old. You could use multiple linear regression to predict the height of a child (dependent variable) using both age and gender as predictors (i.e., two independent variables).

### Multiple Linear Regression Statistics

A common objective of statistical data
analysis
for doctoral research is to make inferences about a population
based upon sample data. The multiple regression model can be used to make
predictions about the dependent variable.

One way to measure the overall predictive accuracy of a multiple regression model is the R-square value. The interpretation of R-square is: "The amount of variance in the dependent variable that can be explained by the model." If the R-square value is 1.0, this means the model explains 100% of the variance and so the model will produce perfect predictive accuracy. This never happens in the real world though. The point is, the closer to 1.0 the R-square value is, the better the model. The closer the R-square value is to 0, the worse the model.

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