# How to do Regression with many replicates of y at each level of x?

#### Modi2020

##### New Member
Hi follows,
I have data that looks as follows:

X, y1, y2, y3, y4

0, 54.241, 127.728, 127.73802, 127.73802
31, 65.132, 127.729, 127.73787, 127.73792
59, 65.364, 127.729, 127.73782, 127.73789

Where y1-y4 are just independent replicates at a given x level.
I could take the averages of y and perform simple linear regression of the averages on x . However, I doubt that that is the most optimal way of doing this. I thought of fitting a random effects model (with replicate as random) to asses the variability between replicates. I have thus used the lmer package in R to do so.
I fitted the following model: lmer(value~X+(1|replicate),data=long_form)
I obtained the following random effects variance components estimates:
Random effects:

Groups Name Variance Std.Dev.

replicate(Intercept) 16.292 4.0364

Residual 100.557 10.0278

I have the following question on this issue:

1) Can some one tell me in lay mans terms what does the variance of 16.292 mean in this case?
2) I assessed the normality of the data and it turned out not normal. The box-cox function suggested a power (2) transformation so I transformed the data but the transformed data is still not normal. Can anyone suggest a workaround for this problem as I still want to fit the above model?

Thank you