# Logistic regression coefficient in not-so-good classification result

I did a Logistic Regression (LR) on a 2-class problem (77.3% negative, 22.7% positive), and the results are as follow:

$\text{logit} (p) = -2.0 + 1.4X_1 + 1.3X_2 + 0.2X_3 - 0.3X_4 - 0.7X_5$

The final model Likelihood Ratio Tests indicated the model is significantly better than the intercept-only model (Chi-square = 21.636, df=5, p = 0.001).

The goodness-of-fit is also indicating the model is good.

Pearson Chi-square = 12.777, df=12, p = 0.385

Deviance Chi-square = 16.007, df=12, p = 0.191

Pseudo R-Square

Cox and Snell .033

Nagelkerke .050

Everything seems ok, but my classification result is not so good. Basically, it classifies everything as negative (Model accuracy = 77.3% same as the baseline).

My question is whether the estimated coefficient from this model is still any good considering its classification performance is not.

I added the ROC of the positive class.

• Please explain how this model "classifies" things. Logistic regression ordinarily lets you estimate probabilities of responses, but it does not involve any form of classification--that's something you add on to the results and there are many different ways to do that. – whuber Mar 29 '17 at 15:05
• I used a cut-off point at 0.5. – user1480478 Mar 29 '17 at 15:06
• From the limited degrees of freedom, it seems that you only have a handful of cases and probably less than 10 in the least-prevalent class. If so you are severely over-fitting; you should have 10-20 of the least-prevalent cases for each predictor variable you are examining, or 50-100 for your model. – EdM Mar 29 '17 at 17:02