# 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?

Your help is greatly appreciated

Thank you

#### Dason

##### Ambassador to the humans
How are the three measurements in the y1 column related? Are they from the same subject?

#### Modi2020

##### New Member
Yes, measurements on the same column belong to the same subject.
Thank you
How are the three measurements in the y1 column related? Are they from the same subject?