Relationship Of Class Attendance And Exam Performance - 275 Words

Relationship Of Class Attendance And Exam Performance (Essay Sample) Content: EconometricsStudents nameCourse nameDateInstructors nameECOM30002 Econometrics1. Consider two random variables X1 and X2 with means 1 = E(X1), 2 = E(X2), variance- covariance matrixSolutionFrom S2=e1Pe/N-2Variance=X1X2=12121222=S2 (X1PX) 1The estimate of the variance predicted by the mean of Y given a value X, is given by X0S2Yn/X0=S21,X0X1px-11X0An estimate of the variance of the predicted value of Y for an individual for a specific value of X, say , is given by X0To obtain the estimate of the predicted value that is Y given X in this case we use X0.S2Y1/X0=S2+S2Yn/X0But r=K=1NPjXJ-XYj-Y K=1NPjXJ-X2 k=1NYj-Y2=SxySxxSyy=rxxrxy=singrxxR2Where Sxy is the covariance between X and Y, rxx is the slope from the regression of X on Y, and ryx is the slope from the regression of Y on XQUESTION 2 * For conditional distributionSuppose x~Np,Let x be portioned as x=x1x2 then the conditional distribution of xi given x1 isN2+21-111X1-1, 2221-11112From FX2,X1=F(X)F(X1)FX=12P-21e-21 (x-)1-1(x- )x~N1,11fx1=1(2)r211-12e-21(x-1)111-1(x1-1)Let Q=x -1-1x-Using the partitioning of x, we haveQ=11122r2e-21Q*Where Q*=Q-QTherefore x2/x1~ +2111x1-1, 22-2111-112 * The n = 1000.Compare the sample means and their variances.Mu () -2Sigma (1) -2 sigma (2)0.4n-10sim-1000 1=2 2=1.2 0=0.222 Mean variance  =0 0.71 0.4  =0.5 1.6 0.005 The condition of unbiased estimator requires that Ax=0Implying that AC1=0 and CA1=0Var (b) =32x1x-1+AC1+CA1+CC1Var (b) =32x1x-1+CC1Varb=32x1x-1+32CC1Both this is equal to varvar=32x1x-1Varb=var+32CC1 Meaning that Varb=var hence unbiased estimator * Omitted variable bias occurs when the estimate is higher than the true parameterFor exa...