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

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

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

It is similar to the t-statistic in linear regression.

In the output of the summary() function for the logistic regression model in R, the z value and Pr(>|z|) columns represent the statistical significance of each coefficient in the model.

The z value is the ratio of the estimated coefficient to its standard error. It measures the number of standard deviations that the estimated coefficient is away from zero. A higher absolute value of z value indicates that the estimated coefficient is more statistically significant.

The Pr(>|z|) column represents the p-value for each coefficient, which is the probability of observing a z value as extreme or more extreme than the observed value, assuming the null hypothesis that the coefficient is zero. A lower p-value indicates that the coefficient is more statistically significant, and a value less than 0.05 is often considered as evidence to reject the null hypothesis.

In the example provided, for the variable disp, the z value is -2.241, and the corresponding Pr(>|z|) is 0.025, which means that the coefficient for disp is statistically significant at the 5% significance level.