# Read the Model Summary

`model.summary()` is the primary diagnostic after fitting. It reports one row per smooth term and a block of overall fit statistics. Learning to read it fluently takes about five minutes and pays off every time you fit a model.


# Fit a two-smooth model

The `wages` dataset records hourly wages alongside `age` and `experience`. Wages are positive and right-skewed, so `wk.Gamma()` is a natural choice.


``` python
import whittaker as wk

data = wk.load_dataset("wages")
```


``` python
# Fit two-smooth Gamma GAM
model = wk.GAM("wage ~ s(age) + s(experience)", family=wk.Gamma()).fit(data)
model.summary()
```


    GAM fit summary
    ============================================================
    Formula:    wage ~ s(age) + s(experience)
    Family:     Gamma(link='log')
    Inference:  GCV
    Observations: 800
    Coefficients: 19

    Parametric coefficients:
      Term                       Estimate    Std.Err    t value    p-value
      ------------------------ ---------- ---------- ---------- ----------
      (Intercept)                  3.7109     0.0084    440.686    < 1e-16

    Approximate significance of smooth terms:
      Term                        EDF Ref.df     Chi.sq    p-value
      ------------------------ ------ ------ ---------- ----------
      s(age)                     3.23      4   2473.551    < 1e-16
      s(experience)              2.82      3    177.907    < 1e-16

    Total EDF:  7.05
    Scale est:  0.056726
    Deviance:   44.9806
    Null dev:   205.9584
    Dev. expl:  78.2%
    GCV score:  0.057230
    AIC:        5881.68
    BIC:        5914.71


# Smooth terms table

Each row in the upper block describes one smooth term.

| Column | Meaning |
|----|----|
| **Name** | The smooth term as written in the formula, e.g. `s(age)` |
| **EDF** | Effective degrees of freedom (how wiggly the fitted smooth actually is) |
| **Ref.df** | Reference degrees of freedom used in the F-test denominator |
| **F** | F-statistic testing whether the smooth differs significantly from zero |
| **p-value** | Two-sided p-value for the F-test where small values indicate a real effect |

EDF = 1 means the smooth collapsed to a straight line. EDF = 5 means it used five degrees of freedom to bend through the data.


# Model statistics

The lower block summarises overall fit.

- **n**: number of observations used in the fit.
- **Family**: the distribution and link function (e.g. `Gamma [log]`).
- **Deviance explained**: the proportion of null deviance accounted for by the model, analogous to R² in OLS.
- **GCV score**: generalized cross-validation score used to select smoothing parameters (lower is better when comparing models on the same data).
- **Scale estimate**: estimated dispersion parameter for the family.


# EDF as a diagnostic

If the EDF of a smooth is close to the maximum allowed by the basis dimension `k`, the basis may be too small to capture the true curve shape. Whittaker will not automatically warn you, but the summary makes it visible: an EDF near `k − 1` is a prompt to refit with a larger `k`. Recipe 23 covers the formal k-index test for basis dimension adequacy.

The `edf` attribute holds one value per smooth term as a list of floats.


``` python
model.edf
```


    [3.227258222729782, 2.8235746255378054]


Compare these values against the default basis dimension (usually `k = 10`, giving a maximum EDF near 9). A value close to the ceiling is a signal to increase `k`.