Table of Contents
Pr(>|z|) in Logistic Regression Output in R is the p-value associated with the z-test statistic for the logistic regression coefficients. This p-value is used to evaluate the significance of each coefficient in the model. If the p-value is less than the significance level (typically 0.05), then the coefficient is statistically significant and can be used to make inferences about the data.
Whenever you perform logistic regression in R, the output of your regression model will be displayed in the following format:
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -17.638452 9.165482 -1.924 0.0543 .
disp -0.004153 0.006621 -0.627 0.5305
drat 4.879396 2.268115 2.151 0.0315 *
The Pr(>|z|) column represents the p-value associated with the value in the z value column.
If the p-value is less than a certain significance level (e.g. α = .05) then this indicates that the predictor variable has a statistically significant relationship with the in the model.
The following example shows how to interpret values in the Pr(>|z|) column for a logistic regression model in practice.
Example: How to Interpret Pr(>|z|) Values
The following code shows how to fit a in R using the built-in mtcars dataset:
#fit logistic regression model
model <- glm(am ~ disp + drat, data=mtcars, family=binomial)
#view model summary
summary(model)
Call:
glm(formula = am ~ disp + drat, family = binomial, data = mtcars)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.5773 -0.2273 -0.1155 0.5196 1.8957
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -17.638452 9.165482 -1.924 0.0543 .
disp -0.004153 0.006621 -0.627 0.5305
drat 4.879396 2.268115 2.151 0.0315 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 43.230 on 31 degrees of freedom
Residual deviance: 21.268 on 29 degrees of freedom
AIC: 27.268
Number of Fisher Scoring iterations: 6
Here’s how to interpret the values in the Pr(>|z|) column:
- The p-value for the predictor variable “disp” is .5305. Since this value is not less than .05, it does not have a statistically significant relationship with the response variable in the model.
- The p-value for the predictor variable “drat” is .0315. Since this value is less than .05, it has a statistically significant relationship with the response variable in the model.
The under the coefficient table tell us that a single asterisk (*) next to the p-value of .0315 means the p-value is statistically significant at α = .05.
How is Pr(>|z|) Calculated?
Here’s how the value for Pr(>|z|) is actually calculated:
Step 1: Calculate the z value
First, we calculate the z value using the following formula:
- z value = Estimate / Std. Error
For example, here’s how to calculate the z value for the predictor variable “drat”:
#calculate z-value 4.879396 / 2.268115 [1] 2.151
Step 2: Calculate the p-value
Next, we calculate the two-tailed p-value. This represents the probability that the absolute value of the normal distribution is greater than 2.151 or less than -2.151.
We can use the following formula in R to calculate this value:
- p-value = 2 * (1-pnorm(z value))
For example, here’s how to calculate the two-tailed p-value for a z-value of 2.151:
#calculate p-value
2*(1-pnorm(2.151))
[1] 0.0314762
Notice that this p-value matches the p-value in the regression output from above.
The following tutorials explain how to fit various regression models in R: