Student or Learner
The variance of the probability distribution of y does not change with each observation. Some observations on y are not more likely to be
further from the regression function than others.
Considering the above sentence I would like to know what the verb " To be further from" means, further Does the underlined part mean that " The probability distribution of y does not change with "no" observation, or it means It doesn't change with all observations but some of them.
"Further from" is a measure of distance. If I have a set of data and 50 is the mean, then a new data point that is 51 is not further from the mean than a point that is 25 would be.
Yes, they mean that some new observations will change the variance and some will not. It does not change with each/all, but it will change with some.