under the assumptions of the linear regression model and cov(Ei,Ej) 0 prove that CON(W,Y):0 under the assumptions of the linear regression model and cov(Ei,Ej) 0 prove that CON(W,Y):0
Which of the following is NOT an assumption of the multiple regression model? Select one: a. E(ei)=0 E ( e i ) = 0 b. The values of each xik are not random and are not exact linear functions of the other explanatory variables. c. cov(yi,yj)=cov(ei,ej)=0;(i≠j) c o v ( y i , y j ) = c o v ( e i , e j ) = 0 ; ( i ≠ j ) d. var(yi)=var(ei)=σ2i
Part A Consider the Simple Linear Regression model. If the COV[X,Y] = 2.4, VAR[X] = 1.2, X-bar = 9.6, and Y-bar = 23.4, then compute the slope coefficient Beta1. Provide your answer with three decimal places of precision, e.g. 0.001. Part B Consider the Simple Linear Regression model. If the COV[X,Y] = 2.4, VAR[X] = 1.2, X-bar = 9.6, and Y-bar = 23.4, then compute the intercept Beta0. Provide your answer with three decimal places of precision, e.g. 0.001.
2. (10pt) Consider a linear regression model without the intercept: Y = BiXiEi, where E(ei) = 0 and V (e;) = a2. What is the LSE of B here?
Consider the multiple regression with three independent variables under the classical linear model assumptions: y Bo+BBx,+B,x, +u 1. You would like to test the hypothesis: H0: B-3B, 1 What is the standard error of B-3B,? (i Write the t-statistic of B-3B ( Define 0,= B-3B.. Write a regression equation that allows you to directly obtain 0, and its standard error.
linear regression model yi= a + bxi +ei calculate 95% confidence interval of b assuming ei ~N(0,o2)
Regression analysis 1.3. Use the statistical model Yi Bo1Xi+ € to show that ei ~NID(0, o2) implies each of the following: (a) E(Y)Bo B1X, (b) 2(Y2, and (c) Cov(Y,Y)= 0, i i' For Parts (b) and (c), use the following definitions of variance and covariance o2(Y Y E(Y)]} Cov(Yi, Y) E{[Y-E(Y)Y- E(Y)] 1.3. Use the statistical model Yi Bo1Xi+ € to show that ei ~NID(0, o2) implies each of the following: (a) E(Y)Bo B1X, (b) 2(Y2, and (c) Cov(Y,Y)= 0,...
4. Consider the simple linear regression model: Vi=Ay+βίζί +Ej, for i=1, . . . , n. Write out the expression for y, β,e, and X such that the model can be written in matrix orim
Simple linear regression model Assumptions: AI E[u] 0 for all i, i1, .., n On average, random component is zero Model runs through expected values of Yand Y A2 E[uaij]-0 for all i and j where i /j COV(IIİlh)- Unobserved component not related across observations E[14"]= for all i All observations have random component dravn from a distribution with the same variance σ2 , f(0,02) A3 var(11i)-σ (Homoskedasticitv) A4 E[Alli] = 0 for all i Random component and covariate not...
Suppose we fit the simple linear regression model (with the usual assumptions) Y = Bo+B1X+ € and get the estimated regression model ♡ = bo+bix What aspect or characteristic of the distribution of Y does o estimate? the value of Y for a given value of X the total variability in Y that is explained by X the population mean number of Y values above the mean of Y when X = 0 the increase in the mean of Y...
5) Consider the simple linear regression model N(0, o2) i = 1,...,n Let g be the mean of the yi, and let â and ß be the MLES of a and B, respectively. Let yi = â-+ Bxi be the fitted values, and let e; = yi -yi be the residuals a) What is Cov(j, B) b) What is Cov(â, ß) c) Show that 1 ei = 0 d) Show that _1 x;e; = 0 e) Show that 1iei =...