Suppose that instead of estimators of the form aX+e , we consider estimators of the form Θˆ=aX and ask for the value of a that m
inimizes the mean squared error. Mimic the derivation you have just seen and find the optimal value of a . Your answer should be an algebraic expression involving some of the constants b , c , d , where b=E[Θ2] , c=E[ΘX] , d=E[X2] .
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Answer:
See below
Step-by-step explanation:
First, I would choose three different points with some distance between. Let's do x = -5, x = 0, and x = 5. Next, I would plug those numbers into the equation, like so:
Next, I would plot the points [(-5, 45), (0, 25), (5, 5)] on an x-y graph. Finally, I would take a ruler, line it up with the three points, and draw a line through those three points, extending from one side of the graph to the other to show the equation is continuous.