If E(ui/X) = 0 is not
sasfied or E(ui/X)
0 then estimate of
and
will be biased.
So ooption first is correct
Consider the regression model: Y = Bo + B,X+u Which of the following assumptions would, if...
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.
2.25 Consider the simple linear regression model y = Bo + B x + E, with E(E) = 0, Var(e) = , and e uncorrelated. a. Show that Cov(Bo, B.) =-TOP/Sr. b. Show that Cov(5, B2)=0. in very short simple way
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...
We consider the regression model Y=Bo + B1X + u sample size of n =946 And we found for a Y=4.75 -0.1748 (0.94) (0.1840) Give the p-value for the test Ho:B1 0 H1:B1 0 (round your answer to 4 digits after the decimal). QUESTION 16 We consider the regression model Y Bo+ B1X u And we found for a sample size of n = 946 Y= 6.318 + 0.24462 (0.44) (0.1620) Give the p-value for the test Ho:B1 0 H1:B1...
are the assumptions behind any multiple regression model? (b). For a multiple regression model Y-Bo + βιΧ. + β2X2 +β3Xs + € where is the error term, to represent the relationship between Y and the four X- variables. We got the following results from the data: Source Sum of Squares degrees of freedom mean squares Regression 1009.92 Residual Total 2204.94 34 And also you are given: Variable X1 Σ.tx-xr 123.74 72.98 12.207 -Pr values -11.02 5.13 X2 X3 Y-intercept is...
f and g
1. Consider the standard bivariate regression: Y = Bo + B,X, + a) What is the above function called? b) What are Y, X, X, Bo, and B, called? Graph an example of the function along with some fake data points (X,Y) and label each of the parts. c) Suppose that we estimate the above function using a sample of data and the ordinary least squares method (OLS). Write down the sample regression function. d) What is...
Consider the following linear regression model 1. For any X x, let Y xBU, where 3 E R*. 2. X is exogenous 3. The probability model is {f(u;0) is a distribution on R: Ef [U] = 0, VAR, [U] = 02,0 > 0}. 4. Sampling model: Y} anidependent sample, sequentially generated using Yi x Ui,where the U IID(0,0) are (i) Let K 0 be a given number. We wish to estimate B using least-squares subject to the constraint 6BK2. Write...
Exercise 4.11 Consider the regression model Y Po PX+u Suppose that you know Bo 1. Derive the formula for the least squares estimator of p The least squares objective function is OA. n (v2-bo-bx?) i-1 Ов. O B. n (M-bo-bX) /# 1 n Click to select your answer and then click Check Answer. Exercise 4.11 OA n Σ (--B,χ?) O B. E (Y-bo-b,X)2 j= 1 n Σ (Υ-Βo-bΧ) 3. j= 1 D. n Σ (Υ-0-b,) i- 1 Click to select...
Suppose assumptions SLR.1-SLR.3 are satisfied and consider a regression model of savings (sav) on income (inc): inc2 xe B1inc + u, where u = Bo sav = Suppose e is a random variable with the following properties: E(einc) 0 Var(elinc) a) Does this regression satisfy the zero conditional mean b) Does this regression satisfy the homoskedasticity assumption (SLR.5)? c) In the real world, why might the variance of savings depend on income? assumption (SLR.4)?
Consider the following regression model: Xi = Bo + Bixi + y; where yi is individual i's University GPA and xi is the individual's high school grades. a. What do you think is in ui? Do you think E[ulx) = 0? Suggest a variable that you think might affect University GPA that isn't included in the regression equation but should be. c. What sign of bias would you expect in an OLS regression of y on x? Briefly explain. d....