Suppose that each setting xi of the independent variables
Chapter , Problem 25(choose chapter or problem)
Suppose that each setting \(x_i\) of the independent variables in a simple least squares problem is duplicated, yielding two independent observations \(Y_{i_1}, Y_{i_2}\). Is it true that the least squares estimates of the intercept and slope can be found by doing a regression of the mean responses of each pair of duplicates, \(\bar{Y}_i=\left(Y_{i_1}+Y_{i_2}\right) / 2\) on the \(x_i\) ? Why or why not?
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