and determine conditions for their local asymptotic stability: dP p2 BP(1 – P) - Z - | dt + p2 dZ p? - -). %3D dt + p2 1004)

O Suppose amultiple Regression Model 9 = B. + R, X1 +. . +RXk+ E ory=xB+E @EStiMate BS . O show that Bis unbiaS.

Consider the following population model for household​ consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is​ consumption, inc is​ income, educ is the education level of household​ head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted​ value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certain

Exercise 21. Assume that we have observed paired data 21,...,n and y₁,..., yn, and we want to describe these data using the model Y₁ = y + E, where e, are i.i.d. with E(₁) = 0. a) Using the least squares method, determine an estimator for the parameter 7. b) Show that your estimator is unbiased.