Consider exploring the effects of violations in assumptions or issues in the data of the OLS (ordinary least squares) regression. Recall, WOLOG, for a regression of dependent variable Y using independent variables or predictors X and X, we have the (population or true) regression model Y = Bo + B1Xi1 + B2X12 + , where Eind N (0,0), i = 1,2,..., n, with unknown quantities [Bo, B, B]. This can be written as y = XB + , with X11 X12 1 X21 X22 y=[Y, YY] X= = [1, 2,..., En]' 1 B=B LB. [1 Xn Xn2 We wish to estimate B, and via OLS, our estimator is = (X'X) X'y. When characterizing the estimator, we can look at its absolute bias, AB = E [A-], mean squared error, MSE = E[(B-B)], and standard error, se = var (B) = {[B-E (B)]}, among others. For each of the violations and/or issues, (i) provide an algorithm to illustrate the violation, and (ii) investigate the effect on the estimators for through any of its density, AB, MSE, and se, whichever may be appropriate. a. Nonlinearity, i.e., the regression model is not linear in the coefficients and/or error term. Consider exploring the effects of violations in assumptions or issues in the data of the OLS (ordinary least squares) regression. Recall, WOLOG, for a regression of dependent variable Y using independent variables or predictors X and X, we have the (population or true) regression model Y = Bo + B1Xi1 + B2X12 + , where Eind N (0,0), i = 1,2,..., n, with unknown quantities [Bo, B, B]. This can be written as y = XB + , with X11 X12 1 X21 X22 y=[Y, YY] X= = [1, 2,..., En]' 1 B=B LB. [1 Xn Xn2 We wish to estimate B, and via OLS, our estimator is = (X'X) X'y. When characterizing the estimator, we can look at its absolute bias, AB = E [A-], mean squared error, MSE = E[(B-B)], and standard error, se = var (B) = {[B-E (B)]}, among others. For each of the violations and/or issues, (i) provide an algorithm to illustrate the violation, and (ii) investigate the effect on the estimators for through any of its density, AB, MSE, and se, whichever may be appropriate. a. Nonlinearity, i.e., the regression model is not linear in the coefficients and/or error term