Question

Assignment 1: Bivariate Regression ECO 321 DUE Thursday, February 20 at the beginning of class. You must submit a hard copy of the assignment. 1. Consider the standard bivariate regression Y B + B,X, + a) Suppose that we estimate the above function using a sample of data and the ordinary least square method (OLS). Write down the sample regression function b) Name each of the components in part (a). Then graph an example of the function along with some data points (X,Y) and label each part. c) What is the relationship between R and Bo, and the relationship between 0 and 17 d) What does it mean for Po and consistent? to be consistent? Under which assumptions are ble and e) Graph an example model with data points showing that EwX:] and Varu o ? f) Graph an example model with data points showing that EUX) = 0 and Varu,X, = d. 8) True or False: Showing that E6,X] +implies that EUX: mean assumption does not hold. 0; therefore, the conditional h) True or False: E|Y|X, Y

Answer 1

As per guidelines, I can answer only 4 option of question

I hope you understand,

standard bivariate regression function - Yi= Bot B, Xi tu; cu Yi = E(Y / X;) +u E(Ylxi) a it is the expected value of Y with ginen / constant values of a Sample requession function | ; = B. + B, xi n ; Y - laps estimation of ElYIX.) Bo - estimahor of Bos R = estimator of By ah sample the estimater estimahor (Bo B) are known as stanshc (Bo B, are know Sample regression function with stochastic random term | $ = 8 + 8x; tu; S uns wi= simple residual teem ima PAE Y; - Ro+B,1itete s y variable Ely1x) Elyltüs X'rawiableti ya

tulationship bw Boo Bo & relation blue B & B, ? Bo is estimate of Bo thus Expected value of ßo is always equal to Bo if so is - unbiased estimator of Bo unbiased mean if we estimate Bo with Bo they - th it approch toward Bo with increase in sample size Bos intercept El Bir slope of regression line By Estimation oLs on sample regression function we got value of Bo Q.B, I here 2212 - Å, = {(X;-Xa) (Y,- Vi et introduce E CxX)2 DIT B, = Edidit. 25= 60; -8) Y; CY-Yi) - Exp2 thnko kila ano = {ni Yi d a nose n (Exp2) Exisin sisamuth wat - Eliyi Eki=0, Eki? 1 Ess2 B = {pi (Bot B, Xotui) E kini = {ki Xi=1 = BoEpit By Elixit Ekių; Ekit Eline Ence = 0 + Be + Eku शिक Exi- deviation from mean Elß, ) = 6 (b) + B Elli Elli) E CÉ, I = By Expected value of Uil to Assumption of CCRM

Similarly with Bo - Bo - ✓- Bit N El Bola 1 Ecy:) - EIB,) = 1 / E (Bot B, xi) - B, t Exi (u Bot B, Ex) BExi - HBO +B, Emir By Emi a Bo V nh Bo and ß, is consistent this means that if the size of sample is increase the variance hos of Bo & is, is decreasing & becomes zero. hot sundere assumptions that if B & B, is unbiased. then increase in sample size will decrease the Variencer to zero.