Question

Consider simple linear regression with n pairs of numbers xi, yi . Let β0 + gx be the least squares line where Ao--gx and β,-rosy/s . În terms of the summary statistics, derive a simple expression for the residual standard deviation [Σ- n-2) 12 where For a question like this one that involves a derivation, after you formulate an algebraic solution, check its validity on some numerical regression examples with small data sets. If you match numerically in some instances, your answer is likely correct. If your theoretical answer doesnt match the numerical cases, go back to review your derivation. Part a) To validate whether you have the correct expression, suppose n = 39, rry-07, sy-1.6 and Sx 0.9. What is your value of the residual SD:

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