Multiple linear regression is a statistical method that is an extension of simple linear regression in which more than one independent variable (X) is used to predict a single dependent variable (Y). The predicted value of Y is a linear transformation of the X variables such that the sum of squared deviations of the observed and predicted Y is a minimum. The computations are more complex, however, because the interrelationships among all the variables must be considered in the weights assigned to the variables. The interpretation of the results of a multiple regression analysis is also more complex for the same reason. With two independent variables the prediction of Y is expressed by the following equation:

Y’_i = b₀ + b₁X_1i + b₂X_2i

This transformation is similar to the linear transformation of two variables discussed in the previous chapter except that the w’s have been replaced with b’s and the X’_i has been replaced with a Y’_i.

The “b” values are called regression weights and are computed in a way that minimizes the sum of squared deviations

Multiple linear regression for Obesity, Inactivity, and diabetics. The relationship between two independent variables, “inactive” and “obesity”, and a dependent variable “diabetics”. R-squared, is a statistical measure used in regression analysis to evaluate the goodness of fit of a regression model. It provides an indication of the proportion of variance in the dependent variable that can be explained by the independent variables in the model. An R-squared value of 0.34 in multiple linear regression indicates that the independent variables included in the model collectively explain about 34% of the variability in the dependent variable.