Question

Heat Power would now like to determine the best subset regression model for the heating bill data using only the independent variables that do not exhibit multicollinearity issues. Based on the best subset output below, what should it be their best subset choice? Model X се 10.07 161.78 61.36 10.15 5.71 50.94 K+1 R-Square Adj. R-Square Std. Error 2 0.87 0.86 26.37 2 0.04 -0.02 74.01 2 0.59 0.56 48.08 3 0.88 0.87 26.15 3 0.91 0.90 23.09 3 0.66 0.61 45.48 4 0.93 0.91 21.00 X X2 X X3 XX X X X3 OX; = Square feet of house, X2 = Type of the heating system OX = Square feet of house, X2 = Age of the heating system, X3 = Age of heating system OX1 = Square feet of house, X2 = Age of the heating system OX2 = Age of the heating system, X3 = Type of heating system

Answer 1

Solution :

We’re looking for a model that has a high adjusted R-squared, a small standard error of the regression, and a Mallows’ Cp close to the number of variables plus constant.

Here model of variable X1 and X3 have large and minimum MSE , Cp value is number of parameter plus constant

Answer :

A. $X_{1}$ = square feet of house, $X_{3}$ = Type of the heating system