Question

normal quantile plot

Hello!

I'm supossed to make a normal quantile plot, and i read that "The basic idea of the normal quantile plot is to compare the data values with the values one would predict for a standard normal distribution".

But I thought that only the residual was normal distributed in linear regression.

Can somebody explain why we suddenly state, that the raw data is normal distributed?

Answer 1

Let consider we have Simple linear regression model

that is we have one predictor only

So, our model is y_i = beta0 + beta1*x_i + epsilon_i ; i = 1, 2, ..., n

and epsilon_i follows N(0, sigma^2)

As, we know a linear combination of normal random variables is itself normal.

So, y_i also follows normal distribution with N(beta0 + beta1*x_i , sigma^2) . These are easy to comute.

That's why we are comparing the data values with the values one would predict for a standard normal distribution.

and this is true for any regression model(not just SLRM).

If you further have problems ask me in the comments.