I proved these exercices for my econometrics class. I just want to make sure that my answer matches. If you can provide proofs and explanation, it will be good. 3.Denoting the residuals from the estimated regression equation by ü,,show that the sum of the erors is equal to zero:0Во + вх, + й,4.Show that:û, where y = Y,- Y and x,х, - хis equivalent to:Consider an estimated simple linear regression model: Y = B + BX+u. Show that the average predicted5.value of the dependent variable, Y , is equal to the sample mean of the dependent variable, Y . That is, show:Σ-ΥпConsider the estimated linear regression model: Y = Bo + B,X, +û,6.Write the expressions for the least squares estimators of the intercept and slope coefficients. Do not derive them.A.В.Suppose that the same dependent variable in (A) is modeled as a function of an alternative independentvariable, denoted by Z. The estimated model is given by: Y, = B^ £Z, + uf, where the * distinguishes theestimates from those in (A).Write the expressions for the least squares estimators of the intercept and slope coefficients.С.Next, suppose the variable Z is a linear function of X. Specifically, let Z, = aX where a is a constant.Considering your results from A and B, show how:A and Ai),andare related in terms of the constant aare related in terms of the constant aScanned with CamScanner

Name: I proved these exercices for my econometrics class. I just want to mak
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Description: I proved these exercices for my econometrics class. I just want to make sure that my answer matches. If you can provide proofs and explanation, it will be good. 3.Denoting the residuals from the estimated regression equation by ü,,show that the sum o