# simple linear regression (predictor)

Consider a simple linear regression model $Y = X\beta + \epsilon$ $\$. Let $Y_O$ be the least square predictor of $Y$ at $X = x_o$ , based on $n$ observations $(X_i ,Y_i)$and $\overline X$ = sample mean for $X_i$

then the standard error of the predictor $Y_O$

a) increases as $x_o$ moves away from $\overline X$

b) decreases as $x_o$ moves closer to 0

This is what I tried :- according to me the answer must be option a) because the standard error of the predictor is given by

$s\sqrt {\frac 1n + \frac {(x_o - \overline x )^2}{\sum {(x_i - \overline x)^2}}}$

so clearly if $x_o$ moves away from $\overline X$ standard error increases, but the source where the answers are given (without explanation) says option 'b' is correct.

I am not able to understand how that is. I think it's a misprint, but still I wanted to confirm if from any approach option b) is more relevant than a)

Your formula, reasoning and conclusion are right, so as you say, a is correct, b is (demonstrably) wrong.
Unfortunately there's not much to add; only if $\bar{x}$ were at $0$ would b be correct, but it would simply say the same thing as a in a different, less general way.