Consider the linear regression modelYt = Bo + B1(x1)e + ..+ Bk(Xx)t + Ut, t 1,... T,where the regressors 1, x1,...,X and errors u satisfy the Gauss-Markov assumptions.Let R? be the (centered) R2 of the regression of xj on all other regressors including aconstant. Show that for the OLS estimators of B1,...Bk it holdsvar ß, =T. Sx(1-R)Remark: The factorRis called the variance inflation factor and is used as an indicator of multicollinearityHint. Use the Frisch-Waugh theorem to partial out all other regressors,

The ideal regression model with various assumptions is given as Description of an ideal dataset…

Answered: Yt = Bo + B1(x1)t + ·…· + Bx(Xx)t + Ue,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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i need help with section b
Consider a simple linear regression model, Y₁ = Bo + B₁X₁ + ₁ for i=1,2,...,n with the usual random error term (&) assumptions. Suppose that hypotheses Ho: P₁ = 0 against H₁:₁ <0 were tested and Ho: B₁ = 0 was rejected. Assume ₁e₁² = 0. ei i) Briefly explain what the conclusion of the test means for the values of Y given the values of X. -1 ii) Draw an example of a scatter plot with the fitted regression line for the problem mentioned above. iii) Calculate and interpret the correlation coefficient for the problem at hand.
Consider the linear model y=B,+B,x,+B,x,,+B,x+B,+u, You estimate the model y =B,+B,x,+B,x, observations and obtain the OLS residuals . You then estimate the auxiliary regression +u based on 123 31 3" 3i 41 The LM statistic +1 4/ you obtain to test the null hypothesis that H:B,=B,=0 is 20.91. What is the R2 of the auxiliary regression? It is not possible to say O 0.17 O 0.175714 0.177203
Consider the linear regression y, = B, + Bx, + u;, i=1,...,n,n+1,..,n+ p where E(u,) = 0. Is it possible to observe a result that E(B,)+ B,, while E(B) = B,-
6. Consider the regression model Yi = βXi + ui, where ui and Xi satisfy the least squares assumptions in Key Concept 4.3. Let β ̄ denote an estimator of β that is constructed as β ̄ = Y ̄/X ̄, where Y ̄ and X ̄ are the sample means of Yi and Xi, respectively. (a) Show that β ̄ is a linear function of Y1 , ..., Yn . (b) Show that β ̄ is conditionally unbiased.
Example 15.11) The following table shows the marks obtained in two tests by 10 students: Marks in Ist Test (X) 8 8. 10 4 7 Marks in 2nd Test (Y) 8 7 7. 10 5 8. 10 6. (a) Find the least square regression line of Y on X. / 7,
Consider the following simple linear regression model, Y; = Po + B₁X₁ + εi, for i=1,2,...,n, where &'s are all independent and normally distributed with E(₁) = 0, and Var(₁) = 0². i) Check whether a statistic Y = Y + B₁ (X₁-X) is an unbiased estimator of the mean of the response variable E(Y) or not. Justify your conclusion.
Consider the regression model y = a + ßx+u, where x is an endogenous variable. a) Write x₁ = x + ê; and show that = x. b) Suppose there are k valid instruments: Z1, Z2, ..., Zk. Let x₁= πo+f1zil + π2Zi2+...+îkzik. Show that the 2SLS estimator is equivalent to an IV estimator using as an instrument: Σ₁₁(&i- Ñ)(vi- V) _ Σ₁(Ri—Ñ)(Yi-Y) Ei=1(xi-x)² 21(®i- Đ)(xi-x) = [Hint: OLS first order conditions imply №₁ ê¡Â¡ = 0 and Σ¼_₁ ê¡= 0.] c) Suppose there is only one instrument z and ✰; = fo+ fizi. Show that the 2SLS estimator is numerically identical to the IV estimator: = Σ₁ (Îi—Ñ)(vi-V) – Σ₁(²₁-7)(vi-V) Σ=1(ât− x)2 Σ₁ (Z₁-7)(xi-x)* n [Hint: Use the result in (b) and plug in â; and ☎ = ñîo+â¦Z.]
1. Consider the following regression model y = x3 + u. (1) Let 3 denote the Ordinary Least Squares (OLS) estimator of B. The so-called Gauss- Markov assumptions are: • MLR.1: The true model in the population is given by (1). • MLR.2: We have a random sample of n observations {(ri, Yi), i = 1, 2, .., n} following the population model in (1). .... • MLR.3: No one explanatory variable can be written as a linear combination of the remaining explanatory variables that is, there is no perfectcollinearity. • MLR.4: In the population, the error u has an expected value of zero given any values of the explanatory variables, that is Elu|x] = 0. • MLR.5: In the population, the error u has the same variance given any values of the explanatory variables, that is Var[u|x] = o? , an unknown finite, positive constant. In the following scenarios, state whether 3 is an unbiased and consistent estimator of 3, and provide a brief justification for your answer in each case - but no formal mathematical…
6. Suppose we estimate a linear regression equation Y; = Bo + B1X; + u; by OLS. (a) Show thatE ûi 0, where the û;'s are the regression residuals. i3D1 (b) Suppose we regress X; on û; by OLS, including a constant term in the regression. Show that the estimated coefficient on û; is equal to zero. (c) Suppose we regress Y; on the predicted value Y; by OLS, including a constant term in the regression. Show that the estimated coefficient on Y; is equal to one. (Hint: the regression residual is defined by û; = Y; – Y; where the predicted value Y; = Bo + B,X;. Here, Bo and B1 are the OLS estimators.)
I need this question completed in 10 minutes with full handwritten working out
A statistics student is asked to estimate Y = Bo + B1X + E. She calculates the following values: Ex = 280, Σ(x₁ - x)² = 350, Σy, = 600, Σ(y, − y) = 1000 Σ(x,x)(y₁ - y) = -630, n = 20 Which of the following is the sample regression equation? OY--55.2-1.8X + e OY 55.2 +1.8X + e OY-55.2+1.8X + e OY 55.2 1.8X + e

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