Extract P-Values for Intercept and Independent Variables of a General Linear Model in R

General linear model does not assume that the variables under consideration are normally distributed, therefore, we can use other probability distributions to create a general linear model. We should actually say that if the data does not follow normal distribution then we can try different distributions using general linear model and check whether the model is appropriate or not. The p-values plays an important role in selecting the best model and we might want to extract them from the model object. This can be done by using coef function.

Example

Consider the below data frame −

 Live Demo

> set.seed(123)
> var1<-rnorm(20,0.5)
> var2<-rnorm(20,1.5)
> var3<-rnorm(20,2.5)
> Response<-rpois(20,2)
> df<-data.frame(var1,var2,var3,Response)
> df

Output

   var1       var2       var3    Response
1 -0.06047565 0.4321763 1.8052930    2
2 0.26982251 1.2820251 2.2920827    1
3 2.05870831 0.4739956 1.2346036    1
4 0.57050839 0.7711088 4.6689560    1
5 0.62928774 0.8749607 3.7079620    1
6 2.21506499 -0.1866933 1.3768914   6
7 0.96091621 2.3377870 2.0971152    1
8 -0.76506123 1.6533731 2.0333446    0
9 -0.18685285 0.3618631 3.2799651    1
10 0.05433803 2.7538149 2.4166309    3
11 1.72408180 1.9264642 2.7533185    2
12 0.85981383 1.2049285 2.4714532    4
13 0.90077145 2.3951257 2.4571295    2
14 0.61068272 2.3781335 3.8686023    3
15 -0.05584113 2.3215811 2.2742290   2
16 2.28691314 2.1886403 4.0164706    2
17 0.99785048 2.0539177 0.9512472    3
18 -1.46661716 1.4380883 3.0846137   3
19 1.20135590 1.1940373 2.6238542    5
20 0.02720859 1.1195290 2.7159416    2

> General_LM<-glm(Response~var1+var2+var3,df,family=poisson())
> summary(General_LM)

Output

Call:
glm(formula = Response ~ var1 + var2 + var3, family = poisson(),
   data = df)
Deviance Residuals:
   Min    1Q    Median    3Q    Max
-1.8886 -0.6977 -0.1502 0.7453 1.4222
Coefficients:
         Estimate    Std.    Error z value Pr(>|z|)
(Intercept) 1.00642    0.50653    1.987     0.0469 *
var1        0.18546    0.16256    1.141     0.2539
var2       -0.04053    0.18234   -0.222     0.8241
var3       -0.10772    0.16206  -0.665      0.5063
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 18.704 on 19 degrees of freedom
Residual deviance: 16.376 on 16 degrees of freedom
AIC: 74.43
Number of Fisher Scoring iterations: 5
> coef(summary(General_LM))[,4]
(Intercept)    var1    var2    var3
0.0469347 0.2539288 0.8241122 0.5062662