Similarly to R-squared, log-likelihood only increases as we add more predictors to a model. In the same way that adjusted R-squared penalizes R-squared for more predictors, there are criteria that penalize the log-likelihood for more predictors.

The two most commonly used are *Akaike information criterion (AIC)* and *Bayesian information criterion (BIC)*. Both AIC and BIC use negative log-likelihood, so we actually want the model with the LOWEST AIC or BIC.

AIC and BIC are similar, but BIC gives a bigger penalty for each additional predictor, so it is used for finding the best “simple” model. This is useful because it makes the model more interpretable. For example:

model1 = sm.OLS.from_formula('rent ~ bedrooms + size_sqft + borough', data=rentals).fit() model2 = sm.OLS.from_formula('rent ~ bedrooms + size_sqft + borough + has_doorman', data=rentals).fit() print(model1.llf) #Output: -43756.418 print(model2.llf) #Output: -43756.017 print(model1.aic) #Output: 87522.837 print(model2.aic) #Output: 87524.034 print(model1.bic) #Output: 87555.423 print(model2.bic) #Output: 87563.137

We see that the log-likelihood for model 2 is slightly larger (better), but the AIC for model 2 is slightly larger (worse), and BIC even more so. Both AIC and BIC would lead us to choose model 1, whereas log-likelihood would lead us to choose model 2.

### Instructions

**1.**

Two different models have been fit for you in **script.py** and saved as `model1`

and `model2`

, respectively. Print out the log-likelihood for both models.

**2.**

Based on the log-likelihood values, which model would you choose? Indicate your answer by setting a variable named `which_model_loglik`

equal to `1`

if you would choose `model1`

and equal to `2`

if you would choose `model2`

.

**3.**

Print out the AIC for `model1`

and `model2`

.

**4.**

Based on the AIC values, which model would you choose? Indicate your answer by setting a variable named `which_model_aic`

equal to `1`

if you would choose `model1`

and equal to `2`

if you would choose `model2`

.

**5.**

Print out the BIC for `model1`

and `model2`

.

**6.**

Based on the BIC values, which model would you choose? Indicate your answer by setting a variable named `which_model_bic`

equal to `1`

if you would choose `model1`

and equal to `2`

if you would choose `model2`

.