Multiple Linear Regression is performed on a data set either to predict the response variable based on the predictor variable, or to study the relationship between the response variable and predictor variables. For example, using linear regression, the crime rate of a state can be explained as a function of demographic factors such as population, education, or male-to-female ratio.
This procedure performs linear regression on the selected data set. This fits a linear model of the form
Y= b0 + b1X1 + b2X2+ .... + bkXk+ e
where, Y is the dependent variable (response) and X1, X2,.. .,Xk are the independent variables (predictors), and e is the random error. b0 , b1, b2, .... bk are known as the regression coefficients, which have to be estimated from the data. The multiple linear regression algorithm in XLMiner chooses regression coefficients to minimize the difference between predicted values and actual values.