Suppose we are given a set of observations on income $X_{i}$ and consumption $Y_{i}$ and we plot all the $(X_{i},Y_{i})$ on a graph. We want to draw a sample regression function as close as possible to the existing yet unknown population regression function. Why is it considered wrong to take $\sum \hat u_{i}$ as small as possible to draw our regression function?
My study book says that this method assigns "equal weights" to the $\hat u_{i}$ which is not accurate. However, I also agree with the least order square method.
Anyone have a specific example to show me that the normal summation method leads to bad estimation?