Final answer:
The multiple linear regression model is used to analyze the relationship between multiple independent variables and a dependent variable. The model is partitioned into two parts, X1 and X2, and the goal is to find the coefficients β1 and β2 that minimize the sum of squared errors.
Step-by-step explanation:
In statistics, the multiple linear regression model is used to analyze the relationship between multiple independent variables and a dependent variable. In this case, the model is partitioned into two parts, where X1 represents the first set of independent variables and X2 represents the second set of independent variables. The coefficients β1 and β2 represent the slopes of the two sets of variables, and ϵ represents the residual error term.
To fit the observed data, the regression model can be expressed as y = Xβ + ϵ = X1β1 + X2β2 + ϵ. The goal is to find the values of β1 and β2 that minimize the sum of squared errors (SSE), creating a line of best fit that accurately predicts the values of y based on the values of X1 and X2.