Example of Best Subsets Regression

Technicians measure heat flux as part of a solar thermal energy test. An energy engineer wants to determine how total heat flux is predicted by other variables: insolation, the position of the east, south, and north focal points, and the time of day.

To select a group of likely models for further analysis, the technicians use best subsets regression. In Minitab, best subsets regression uses the maximum R2 criterion to select likely models.

  1. Open the sample data, ThermalEnergyTest.MTW.
  2. Choose Stat > Regression > Regression > Best Subsets.
  3. In Response, enter 'Heat Flux'.
  4. In Free predictors, enter Insolation-'Time of Day'.
  5. Click OK.

Interpret the results

The technicians identify several models to examine further. The model with all 5 predictors has the lowest value of S and the highest value of adjusted R2, approximately 8 and 88% respectively. One of the models with 4 predictors has the smallest value of Mallows' Cp, 5.8. A model with 2 predictors and a model with 3 predictors both have the highest predicted R2, which is approximately 81.4%. Before the technicians choose a final model, they examine the models for violations of the regression assumptions using residual plots and other diagnostic measures.

Best Subsets Regression: Heat Flux versus Insolation, East, South, North, ...

Response is Heat Flux T I i n m s e o l o a S N f t E o o i a u r D R-Sq R-Sq Mallows o s t t a Vars R-Sq (adj) (pred) Cp S n t h h y 1 72.1 71.0 66.9 38.5 12.328 X 1 39.4 37.1 26.3 112.7 18.154 X 2 85.9 84.8 81.4 9.1 8.9321 X X 2 82.0 80.6 74.2 17.8 10.076 X X 3 87.4 85.9 79.0 7.6 8.5978 X X X 3 86.5 84.9 81.4 9.7 8.9110 X X X 4 89.1 87.3 80.6 5.8 8.1698 X X X X 4 88.0 86.0 79.3 8.2 8.5550 X X X X 5 89.9 87.7 78.8 6.0 8.0390 X X X X X
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