Model Selection
Two systematic methods for variable selection. Both use the same call
pattern as ravix.ols() — pass a formula and DataFrame
directly.
Stepwise — ravix.stepwise()
SW1 = ravix.stepwise("Price ~ .", df, direction = "both")
SW1.summary()Summary of OLS Regression Analysis:
======================================================
Coefficients:
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Estimate Std. Error t-value p-value
Intercept 15.568 3.8002 4.097 4.23e-05 ***
Accommodates 12.798 0.51440 24.880 < 2e-16 ***
Bathrooms 12.657 1.0325 12.259 < 2e-16 ***
HostListings 0.39391 0.024465 16.101 < 2e-16 ***
Deposit 0.060696 0.0052196 11.629 < 2e-16 ***
Bedrooms 8.5485 0.94133 9.081 < 2e-16 ***
MinNights 2.0375 0.35092 5.806 6.58e-09 ***
ExtraPeople -0.17785 0.033987 -5.233 1.70e-07 ***
Beds 3.2672 0.66959 4.879 1.08e-06 ***
ResponseRate -12.962 3.5793 -3.621 0.0003 ***
CleaningFee 0.078094 0.023349 3.345 0.0008 ***
FeeMissing 2.2486 0.93516 2.404 0.0162 *
MaxNights -0.0014906 0.0007393 -2.016 0.0438 *
Model Statistics:
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Residual Std. Error: 40.3219
R-squared: 0.4764 AIC: 106115.38
Adj. R-squared: 0.4758 BIC: 106209.59
F-statistic: 785.2638 on 12 and 10357 DF, p-value: < 2e-16
======================================================SW2 = ravix.stepwise("Price ~ .", df, direction = "both", metric="bic", verbose = True)Initial BIC = 112808.1938
Step 1: add Accommodates (BIC=107077.3266)
Step 2: add Bathrooms (BIC=106822.1724)
Step 3: add HostListings (BIC=106607.1197)
Step 4: add Deposit (BIC=106411.2468)
Step 5: add Bedrooms (BIC=106277.3118)
Step 6: add MinNights (BIC=106241.1347)
Step 7: add ExtraPeople (BIC=106219.6968)
Step 8: add Beds (BIC=106205.0822)
Step 9: add ResponseRate (BIC=106200.2787)
No improvement found. Stopping at step 10.
Final BIC = 106200.2787Parameters
| Parameter | Default | Description |
|---|---|---|
method |
"ols" |
"ols", "logistic", or
"poisson" |
direction |
"backward" |
"both", "forward", or
"backward" |
metric |
"aic" |
"aic", "bic", "adjr2", or
"pvalue" |
Best subset — ravix.bsr()
bsr_model = ravix.bsr("Price ~ .", df)Plot best subset results — ravix.plot_bsr()
ravix.plot_bsr(bsr_model)
AIC vs BIC
| Metric | Penalty | Best for |
|---|---|---|
aic |
2k | Predictive accuracy |
bic |
k · ln(n) | Parsimony and interpretation |
Textbook reference: Model selection is covered in Chapter 9 of Applied Linear Regression for Business Analytics with Python.