3.4 Problems 1. Consider the dataset {(0,0), (1,3), (2,2), (3,5)) and the candid

Question

3.4 Problems 1. Consider the dataset {(0,0), (1,3), (2,2), (3,5)) and the candidate model f(z) = 1+1 for the relationship between z and y (a) Determine the sum of absolute residuals lel and the sum of squared residuals (b) Find a "better" model g(x)ab with a lower sum of squared residuals. (c) One of the issues with the sum of absolute residuals is that it can behave weirdly and be hard to minimize. Sometimes slight changes in a or b have no effect on the sum. Explain why this is the case in the above dataset by sketching the graph and the candidate model with a1 and b . Find another model where you slightly change one or both of the parameters and get the same sum of absolute residuals

Explanation / Answer

a)

b)

this will be simple linear regression

y^ = 0.4 + 1.4 x

a = 1.4 , b = 0.4

x y y^ ei |ei| e^2 0 0 1 -1 1 1 1 3 2 1 1 1 2 2 3 -1 1 1 3 5 4 1 1 1 sum 4 4

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