How to Determine Which Model Has a Better Fit — Through One Example

 











1. Deviance Residuals

These are the differences between observed and predicted values, adjusted for the model's distribution. The summary shows:

  • Min: -6.5037
  • 1Q (1st Quartile): -1.5778
  • Median: -0.1833
  • 3Q (3rd Quartile): 1.3519
  • Max: 6.3167

These values help assess the symmetry and spread of residuals. Ideally, they should be symmetrically distributed around zero.

🔹 2. Dispersion Parameter

  • Value: 6.437133
  • For a Gaussian (normal) model, this is the estimated variance of the residuals. It reflects how much the data points deviate from the model's predictions.

🔹 3. Null Deviance

  • Value: 917.69 (on 107 degrees of freedom)
  • This measures the deviance (lack of fit) of a model with no predictors (only the intercept). It serves as a baseline for comparison.

🔹 4. Residual Deviance

  • Value: 682.34 (on 106 degrees of freedom)
  • This is the deviance of the fitted model (with predictors). A large reduction from the null deviance indicates that the predictor(s) (in this case, age) improve the model fit.

🔹 5. AIC (Akaike Information Criterion)

  • Value: 511.58
  • AIC balances model fit and complexity. Lower AIC values indicate a better model, penalizing for adding too many predictors.



MetricModel AModel BInterpretation
Residual Deviance682.34541.87Lower is better — Model B fits better.
AIC511.58488.68Lower AIC suggests Model B is preferred.
Null Deviance917.69917.69Same for both — baseline model.
Dispersion6.445.16Slightly lower in Model B — better variance explanation.

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