# Is it possible to get too small McFadden R^2 while at least one variable is significant?

I am quite new in logistic regression. I tried to apply a logistic regression on a dataset with 3 independent variables: Gender (Categorical- either male or female), Freq_A and Freq_B (continious variables between 0 and 1). My dependent variable is binary. Either 0 or 1. Here is a couple of lines form my dataset:

     Gender       Freq_A       Freq_B Labels
1    Female 5.842289e-03 9.090465e-03      0
2      Male 3.180251e-03 4.009848e-03      1
3      Male 2.060638e-05 2.365917e-04      0
4      Male 1.930360e-02 3.868656e-03      0
5    Female 2.551375e-03 1.110913e-02      0
6    Female 3.564216e-02 3.755856e-02      1


Let me first show you what I did so far:

fname = 'logreg_input.csv'
is.factor(mydata$$Freq_A) # FALSE is.factor(mydata$$Freq_B) # FALSE
is.factor(mydata$Gender) # TRUE train <- mydata[1:1800,] test <- mydata[1801:2000,] model <- glm(Labels ~.,family=binomial(link='logit'),data=train) summary(model)  This is what I got: Call: glm(formula = Labels ~ ., family = binomial(link = "logit"), data = train) Deviance Residuals: Min 1Q Median 3Q Max -1.180 -1.134 -1.006 1.188 1.520 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -0.38513 0.07412 -5.196 2.04e-07 *** GenderMale 0.39087 0.09691 4.033 5.50e-05 *** Freq_A -0.97515 0.70525 -1.383 0.167 Freq_B -0.13894 0.55444 -0.251 0.802 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 2478.1 on 1799 degrees of freedom Residual deviance: 2460.8 on 1796 degrees of freedom AIC: 2468.8 Number of Fisher Scoring iterations: 4  When I look at this, I see the GenderMale is an important variable to explain the variance in the model. (because its significant) But then, I wanted to see how much the model explains the variance. I found that McFadden R2 is somehow similar to R2 value for Linear Regression. Therefore I measured the McFadden R2 value of the model above: library(pscl) pR2(model)  And result is :  llh llhNull G2 McFadden r2ML r2CU -1.230380e+03 -1.239047e+03 1.733430e+01 6.995017e-03 9.583948e-03 1.281971e-02  So, As McFadden R2 value I got 6.995017e-03 which is almost zero. Is that make sense to have such a small R2 value ? What does this value says about my model? • You have a sample size of about 1800 if I understand this correctly and are trying to predict some binary response. In many fields it's common that significance at conventional levels (given the sample size) goes hand in hand with poor explanatory power as measured crudely by substitutes for$R^2\$. I am not sure what answer you seek here, but there is no obvious reason to doubt the software or that you used it correctly. – Nick Cox May 21 at 9:40