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)

Correlation Plot / Matrix High correlations among the predictors. (Passengers and Cabins is very problematic) Passengers/Cabins: r=.976 Tonnage / Cabins: r=.949 Tonnage / Passengers: r=.945 Consider model with Predictors: Age, Tonnage, Passdens, Cabins, Length

Data – First 20 Cases

Full Model (5 Predictors, 6 Parameters, n=158)

Backward Elimination – Model Based AIC (minimize)

Forward Selection (AIC Based)

Stepwise Regression (AIC Based)

Summary of Automated Models Backward Elimination Drop Age (AIC drops from 9.09 to 7.24) Drop Tonnage (AIC drops from 7.24 to 5.52) Stop: Keep Passdens, Length, Cabins Forward Selection Add Cabins (AIC drops from 397.18 to 28.82) Add Length (AIC drops from 28.82 to 9.87) Add Passdens (AIC drops from 9.87 to 5.52) Stepwise – Same as Forward Selection

All Possible (Subset) Regressions

All Possible (Subset) Regressions (Best 4 per Grp)

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 Very similar coefficients for the 2 data sets

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 (k=10) – Full Model