Regression Model Building

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Presentation transcript:

Regression Model Building Predicting Number of Crew Members of Cruise Ships

Data Description n=158 Cruise Ships Dependent Variable – Crew Size (100s) Potential Predictor Variables Age (2013 – Year Built) Tonnage (1000s of Tons) Passengers (100s) Length (100s of feet) Cabins (100s) Passenger Density (Passengers/Space)

Data – First 20 Cases

Full Model (6 Predictors, 7 Parameters, n=158)

Backward Elimination – Model Based AIC (minimize)

Forward Selection (AIC Based)

Stepwise Regression (AIC Based)

Summary of Automated Models Backward Elimination Drop Passenger Density (AIC drops from 1.055 to -0.943) Drop Age (AIC drops from -0.943 to -2.062) Stop: Keep Tonnage, Passengers, Length, Cabins Forward Selection Add Cabins (AIC drops from 397.18 to 28.82) Add Length (AIC drops from 28.82 to 9.8661) Add Passengers (AIC drops from 9.8661 to -0.0565) Add Tonnage (AIC drops from -0.0565 to -2.06) Stepwise – Same as Forward Selection

All Possible (Subset) Regressions

All Possible (Subset) Regressions (Best 4 per Grp) BIC Adj-R2 Cp

Cross-Validation Hold-out Sample (Training Sample = 100, Validation = 58) Fit Model on Training Sample, and obtain Regression Estimates Apply Regression Estimates from Training Sample to Validation Sample X levels for Predicted  MSEP = sum(obs-pred)2/n Fit Model on Validation Sample and Compare regression coefficients with model for Training Sample PRESS Statistic (Delete observations 1-at-a-time) Fit model with each observation deleted 1-at-a-time Obtain Residual for each observation when it was deleted PRESS = sum(obs-pred(deleted))2 K-fold Cross-validation Extension of PRESS to where K groups of cases are deleted Useful for computationally intensive models

Hold-Out Sample – nin = 100 nout = 58 Coefficients keep signs, but significance levels change a lot. See Tonnage and Length.

Testing Bias = 0 from Training data to Validation

PRESS Statistic Model appears to be valid, very little difference between PRESS/n and MS(Resid)

K-fold Cross-Validation Results (k=10)