Lets say I have continuous y and x variable and I run a linear regression:
mdl1<-lm(y ~ x)
A generalised linear model should also give me the same parameters value if I do not specify the error structure (i.e. by default it assumes that the error structure is Gaussian)
mdl2<-glm(y ~ x)
Both the above model should give me the same results (since in the mdl2, by default the error structure is gaussian)
My question is if the residuals are not normally distributed in the mdl1 (i.e. I do a shapiro.wilk test on mdl1 residuals, which gives me a p-value of 0.02),
shapiro.test(rstandard(mdl1)
then in the glm what error family do I specify considering both y and x are continuous. What my understanding was I can specify family=poisson or family=binomial if my response variable was either count or proportion.
mdl3<-glm(y ~ x,family="poisson") # when y is count data
mdl4<-glm(y ~ x,family="binomial") # when y is proportion data
But in case of response variable being continuous and errors not normally distributed what error structure do I need to give?
mdl5<-glm(y ~ x, family=?????) # y is continuous data
