Tiêu đề H Variable Selection with Linear Regression.pdf ✅

IE 7275 Data Mining in Engineering • Department of Mechanical and Industrial Engineering • Northeastern University • © 2020 3/19/2024 1 Variable Selection Using Multiple Linear Regression Sagar Kamarthi Northeastern University [email protected]
IE 7275 Data Mining in Engineering • Department of Mechanical and Industrial Engineering • Northeastern University • © 2020 2 Example problem  We are building a model for car price prediction  Let our training data contain 4 predictors (d = 4)  Miles driven (X1)  Number of seats (X2)  Miles per gallon (X3)  Age of the car (X4)  The target variable (y) is the price of the car
IE 7275 Data Mining in Engineering • Department of Mechanical and Industrial Engineering • Northeastern University • © 2020 3/19/2024 3 Exhaustive Search Sagar Kamarthi Northeastern University [email protected]
IE 7275 Data Mining in Engineering • Department of Mechanical and Industrial Engineering • Northeastern University • © 2023 4 Exhaustive search Step 1: Let S0 be the null model with no predictors. It simply returns the sample mean of response variable values of observations in the dataset. Step 2: For k = 1, 2, ..., d: Fit all possible models SSkk rr with k predictors, where r = 1, 2, ..., dd kk =dCk ; then select the model with SSkk ∗ with the lowest SSE or biggest R2 Step 3: Using cross-validation test error, R2 adj, Mallow’s CP, AIC, or BIC, select the winning model among {SSkk ∗ | k = 0, 1, 2, ..., d}