Exam II – Regression

[Dariusz]

Exam II – Regression

[Anonymous]

Hi,
I’m preparing for Exam II.
And I have found something unclear to me in Regression chapter.
It concerns prediction within regression.
What is the difference between “standard error of prediction mean” and “standard error of prediction”?
It is written very vaguely in the handbook. It is in II.F.6 chapter of the handbook.
Mukul, maybe you would have an idea of how to shed light on this issue.
d.

[Anonymous]

You are right, it is explained a bit poorly in the Handbook.

What linear regression gives us is an equation of the following form:

y = beta*x + constant + an error variable.

Let Y^ (or y-hat, as used in the handbook) be the value ‘predicted’ by the equation above. Y is the actual observed value of the variable y. In this case, if our regression model were 100% accurate, there would be no difference between Y^ and Y. But there is a difference, which is the error variable, or epsilon. Graphically, this means that the regression line is a straight line, and the actual variables are dots scattered around this central line. The ‘error’ is represented by the distance between the actual observations and line itself. Now the way the regression equation is determined is such that the summation of the epsilons is zero. We can determine how ‘good’ our regression line is by calculating the standard deviation of the epsilons. This standard deviation is called ‘standard error’.

What the handbook is saying is that there is a difference between the standard error of the error term (epsilon) and the standard deviation of the predicted Y^ variable. The total variation of the observed value therefore is equal to the standard error of the error term, plus the standard deviation of the predicted Y variable. The former is being called the standard error of prediction mean and the latter the standard error of prediction.

I seriously dowubt if there will be a question on this,or using this rather arcane terminology. But it is useful to know.

[Author]

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