Hi, I need help for this questions. It is statistics simple regression. Please answer and follow the steps. Thank you! Will upvote if it is correct.

Exercise 1 Consider the simple regression model 3/,- = 3150i + 61-,2' = 1, . . . ,n. The GaussMarkov conditions hold.AWe will nd the predicted value of Y0 (a new observation) by minimizing the meansquared error, E(Yo Yo)? We will follow these steps: 1. Assume that the predictor assumption is a linear combination (weighted average) of the observed yi's, i.e. Yo = 221:1 aiYi, where the ags are the weights. We want this predictor to be unbiased, EYO = 51330. Find the constraints that must hold in order for 1% to be unbiased. 2. Now we will minimize the the meansquared error, E (Y0 170)? It will be easier however to minimize var(YO YO). The two minimizations are the same. Why? 3. Now minimize var(Yo Yo) subject to the constraints you found in part (1). Your goal is to nd the weights ags and nally show that the predicted value is Yo = 370 if? 9:: Note: We will show later i=1 i that this is equal to the predicted value given by least squares