- #1
stats_student
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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