Question: Consider the linear model y = Bo+ Bix + , where x is the exogenous variable, y is the endogenous variable, So and B1 are

Consider the linear model y = Bo+ Bix + , where

Consider the linear model y = Bo+ Bix + , where x is the exogenous variable, y is the endogenous variable, So and B1 are parameters, and & is a random variable. a) Construct the formulas for the values of the parameters such that it fits the model to the data set (xi]i=1 using the Ordinary Least Squares criteria. Show all your work. b) Assume that the random variable & is such that E[ ] = E[ex] = 0. Construct the formulas for the values of the parameters such that it fits the model to the data set (x]i=1 using the Method of Moments criteria. Show all your work. c) Assume that the random variable s is normally distributed with a mean of 0 and a standard deviation of o', and it is independent of x. Construct the formulas for the values of the parameters such that it fits the model to the data set (xi]= using the Maximum Likelihood criteria. Show all your work. d) Assume that the random variable & is normally distributed with a mean of 0 and a standard deviation of o', and it is independent of x. Estimate the value of o using the Maximum Likelihood criteria. Show all your work

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