I've built a glm model in R and have tested it using a testing and training group so am confident it works well. The results from R are:
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -2.781e+00 1.677e-02 -165.789 < 2e-16 *** Coeff_A 1.663e-05 5.438e-06 3.059 0.00222 ** log(Coeff_B) 8.925e-01 1.023e-02 87.245 < 2e-16 *** log(Coeff_C) -3.978e-01 7.695e-03 -51.689 < 2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for quasibinomial family taken to be 0.9995149) Null deviance: 256600 on 671266 degrees of freedom Residual deviance: 237230 on 671263 degrees of freedom AIC: NA
All the p values for the coefficients are small as expected.
Looking at this question (Interpreting Residual and Null Deviance in GLM R), I should be able to calculate if the null hypothesis holds using the following equation:
p-value = 1 - pchisq(deviance, degrees of freedom)
Sticking this in gives:
1 - pchisq(256600, 671266)  1
So am I correct in thinking the null hypothesis cannot be rejected here, even though the p values for all coefficients are so small or have I misinterpreted how to calculate this?