“Understanding and Applying Multiple Regression ”

This article is part of the series :

“Getting Started with Machine Learning: A Step-by-Step Guide”

Multiple regression is a statistical technique used to model the relationship between a dependent variable and two or more independent variables. The goal of multiple regression is to find the best fitting line or curve (called the regression line or curve) that describes the relationship between the dependent variable and the independent variables.

To understand multiple regression, it is helpful to first understand simple linear regression, which is a statistical technique used to model the relationship between a dependent variable and a single independent variable. In simple linear regression, we try to fit a straight line to the data, where the line represents the relationship between the dependent variable (Y) and the independent variable (X). The equation for a simple linear regression line is:

Y = a + bX

Where Y is the dependent variable, X is the independent variable, a is the intercept (the point where the line crosses the Y-axis), and b is the slope (the change in Y for every unit change in X).

Multiple regression is an extension of simple linear regression, where we have two or more independent variables (X1, X2, X3, etc.). In multiple regression, we try to fit a curve to the data, where the curve represents the relationship between the dependent variable (Y) and the independent variables (X1, X2, X3, etc.). The equation for a multiple regression curve is:

Y = a + b1X1 + b2X2 + b3X3 + …

Where Y is the dependent variable, X1, X2, X3, etc. are the independent variables, a is the intercept, and b1, b2, b3, etc. are the slopes. The slope b1 represents the change in Y for every unit change in X1, while holding X2, X3, etc. constant. Similarly, the slope b2 represents the change in Y for every unit change in X2, while holding X1, X3, etc. constant, and so on.

An example of multiple regression is a study in which the dependent variable is the body length of a mouse, and the independent variables are mouse weight and tail length. To perform multiple regression in this case, we would collect data on the body length, weight, and tail length of a sample of mice, and then use statistical software to fit a multiple regression curve to the data.

To interpret the results of multiple regression, we can examine the coefficients (b1, b2, b3, etc.) and their corresponding p-values. The coefficient represents the change in the dependent variable (Y) for every unit change in the independent variable, while holding the other independent variables constant.

For example, in the mouse study, if the coefficient for weight (b1) is 0.5, it means that for every 1 gram increase in weight, the body length of the mouse is expected to increase by 0.5 millimeters, while holding the tail length constant. The p-value is a measure of the statistical significance of the coefficient, and indicates the probability that the relationship between the dependent and independent variables is due to chance. A p-value of less than 0.05 is considered statistically significant, which means that we can be 95% confident that the relationship between the variables is real and not due to chance.

It is important to note that multiple regression assumes that there is a linear relationship between the dependent and independent variables. This means that the change in the dependent variable (Y) is constant for every unit change in the independent variables (X1, X2, X3, etc.). If there is a nonlinear relationship between the variables, multiple regression may not be the most appropriate statistical technique.

In conclusion, multiple regression is a statistical technique used to model the relationship between a dependent variable and two or more independent variables. It is an extension of simple linear regression, where we try to fit a curve to the data that represents the relationship between the dependent variable and the independent variables.

The equation for a multiple regression curve is Y = a + b1X1 + b2X2 + b3X3 + …, where Y is the dependent variable, X1, X2, X3, etc. are the independent variables, a is the intercept, and b1, b2, b3, etc. are the slopes. To interpret the results of multiple regression, we can examine the coefficients and their corresponding p-values.

The coefficient represents the change in the dependent variable for every unit change in the independent variable, while holding the other independent variables constant. The p-value is a measure of the statistical significance of the coefficient, and indicates the probability that the relationship between the variables is due to chance. Multiple regression assumes that there is a linear relationship between the dependent and independent variables. If there is a nonlinear relationship between the variables, multiple regression may not be the most appropriate statistical technique.

This article is part of the series :

“Getting Started with Machine Learning: A Step-by-Step Guide”