Boosted Regression (Boosting): An introductory tutorial and a Stata ...

BoostingLinear RegressionFitted y Values0 10 20 30 40 500 10 20 30 40 50 0 10 20 30 40 50Actual y ValuesGraphs by Regression MethodFigure 5: A Calibration plot for the linear regression example: Fitted versus actual valuesfor both linear regression and boosting. The Boosting model is much better calibrated.When working with linear regressions it is common to look at coefficients toassess how a variable affects the outcome. In boosted regression one looks at theinfluence of all variables. The influences are given in percentages. Specifying influencein the Stata command listed in equation (2) gives the following output:x1 30.9%x2 68.3%x3 0.67%x4 0.08%Table 1: Influence of each variable (Percent)Variables x 2 and x 1 are most influential. The other variables have almost no influence.Given that there is weak relation between y and x 3 and no relation between y and x 4 , it isnice to see that the influence of x 3 is larger than that of x 4 .20