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## Homework Statement

note a linear regression model with the response variable Y=(Y1..Yn) on a predictor variable X=(X1..Xn). the least squares estimates of the intercept and slope a(hat) and B(hat) are the values that minimize the function: (see attached image)

and the problem reads on further -

further predicted values equal y(hat)(x)=a(hat)+b(hat)x (note y(hat) is meant to be read as a function of x)

i have been asked to find y(hat)(Xbar), where X(bar) is the average of the Xi's. (note y(hat) is meant to be read as a function of Xbar).

i'm not sure where to start with this question. advice as to whether i'm on the right track is all i need for now.

so i was thinking that i could use the fact that

a(hat) = Y(bar)-B(hat)X(bar) and B(hat) = (sum) (Xi-X(bar))(Yi-Y(bar)) /(sum) (Xi-X(bar))^2

but i'm not exactly sure how to solve for y(hat)X(bar) -(yhat as a function of Xbar)

should i be trying to get a equation with only a(hat) , b(hat) , and Xbar?

Thanks for the help - apologies for poor notation