# What is z value and Pr(>|z|) in logistic regression

#1

I am currently working on logistic regression in R and I have trained the model but when I am looking at summary of model, I am not able to understand what is z value and Pr(>|z|) explains ?

data(mtcars)
names(mtcars)
model1<-glm(formula=vs~wt+disp,data=mtcars,family=“binomial”)
summary(model1)

Call:
glm(formula = vs ~ wt + disp, family = “binomial”, data = mtcars)

Deviance Residuals:
Min 1Q Median 3Q Max
-1.67506 -0.28444 -0.08401 0.57281 2.08234

## Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 1.60859 2.43903 0.660 0.510 wt 1.62635 1.49068 1.091 0.275 disp -0.03443 0.01536 -2.241 0.025 *

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 43.86  on 31  degrees of freedom


Residual deviance: 21.40 on 29 degrees of freedom
AIC: 27.4

Number of Fisher Scoring iterations: 6

#2

The z-value is the regression coefficient divided by standard error. If the z-value is too big in magnitude, it indicates that the corresponding true regression coefficient is not 0 and the corresponding X-variable matters. A good rule of thumb is to use a cut-off value of 2 which approximately corresponds to a two-sided hypothesis test with a significance level of \alpha=0.05.

Thanks,
Mark