Significance Test for Logistic Regression
We can decide whether there is any significant relationship between the dependent variable y and the independent variables xk (k = 1, 2, ..., p) in the logistic regression equation. In particular, if any of the null hypothesis that βk = 0 (k = 1, 2, ..., p) is valid, then xk is statistically insignificant in the logistic regression model.
Problem
At .05 significance level, decide if any of the independent variables in the logistic regression model of vehicle transmission in data set mtcars is statistically insignificant.
Solution
We apply the function glm to a formula that describes the transmission type (am) by the horsepower (hp) and weight (wt). This creates a generalized linear model (GLM) in the binomial family.
We then print out the summary of the generalized linear model and check for the p-values of the hp and wt variables.
Call:
glm(formula = am ~ hp + wt, family = binomial, data = mtcars)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.2537 -0.1568 -0.0168 0.1543 1.3449
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 18.8663 7.4436 2.53 0.0113 *
hp 0.0363 0.0177 2.04 0.0409 *
wt -8.0835 3.0687 -2.63 0.0084 **
---
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: 10.059 on 29 degrees of freedom
AIC: 16.06
Number of Fisher Scoring iterations: 8
Answer
As the p-values of the hp and wt variables are both less than 0.05, neither hp or wt is insignificant in the logistic regression model.
Note
Further detail of the function summary for the generalized linear model can be found in the R documentation.
