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5) Simulate data according to the following. Please provide a log file and any supporting exhibits: x = 12 ,50 Y=1+2X + e e N(0,1) a) Provide an estimate of the coefficients in y BB2x +E b) Are B1 B2 near the true values? ) Store the coefficients in a matrix 8 d) Repeat the simulation 100 times, estimating the equation and storing the coefficients each time e) What is the distribution of simulated coefficients B.B2? a. b. c. Mean Standard Deviation Relate these to the true values of the coefficients and the first two moments of the OLS estimator
math   Statistics-And-Probability   
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e rnorm (50,0,1) Beta2hat-(sum (X*Y)-50 mean (X) mean (Y)) /sum ( (X-mean (X))A2) Betalhat mean (Y)-Beta2hat mean (X) #The .Values of coefficients are Betalhat [11 1.260601 Beta2hat [11 1.99297 #0. b)-yes,,betalhat and beta2hat are near to their true values but slightly differ 2/11 992970 Frst and second row of BetaMatrix represent the. estimate of betal and beta2 respectively. meanbe 78654 mearbeta2 99916 0.> e-rnorm(50, o, 1) Beta2hat (sum (X*Y)-50*mean (X) *mean (Y) )/sum ( (X-man (X) >Betalhat-mean (Y) -Beta2hat*mean (X) > The values of coefficients are Betalhat [11 1.260601 Beta2hat [11 1.99297 > #Q . b) yes ,betalhat and beta2hat are near to their true values butl slightly differ. > B#coeffient Matrix ,1.260601 2,1 1.992970 BetaMatrix=matrix (nrow=2, ncol=100) for 100 Be 2hat mean First and second row of BetaMatrix: ep esent the estimate of beta and ta2.espectively. meanbetai mean (BetaMatrix meanbeta2 1.99916 BetaMa SDbe Dbeta2 va

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