Homework Answers
The Assumptions for the OLS (Ordinary LEast Squares) are:
1) The regression model should be linear in parameters. This condition is fulfiled.
2) The expected value of stochastic term should be zero.This may not be always true.
3) The error term is homoskedastic i.e. the variance is same for the whole sample.
4) The correlation between x variable and error term should be zero. But this condition may not fulfiled here.
5) There should be no autocorrelation among the disturbance. This is true for the given model.
6) The error term should be normally distributed with mean zero and variance equal to 1. This condition is satisfied in the model.
7) There should be no specification biased in the model. This may or may not be true in the model as the intercept has been dropped. There should be a robust argument in favor of dropping such a crucial parameter from the model.
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Suppose we have a regression model Yi = bXi + Ei where Y = X =...
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4. Consider the model yi-β +82i + ei. Find the OLS estimator for β.
4. Consider the model yi-β +82i + ei. Find the OLS estimator for β.
Consider the regression model given by: Yi = βo + β1Xi + β2Zi+ ui Suppose that...
Consider the regression model given by: Yi = βo + β1Xi + β2Zi+ ui Suppose that an econometrician wishes to test the null hypothesis given by: Ho: β1 + β2 = 0 Use this null hypothesis to specify a restricted form of the regression model (in a form that may be estimated using an OLS estimation procedure). State the equation that you could estimate as the restricted version of this model.
3. Consider the linear model: Yİ , n where E(Ei)-0. Further α +Ari + Ei for...
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Consider the simple regression model yi= B1+B2xi2+ei . Suppose N=5 and the values of xi2 are...
Consider the simple regression model yi= B1+B2xi2+ei . Suppose N=5 and the values of xi2 are (1,2,3,4,5). Let the true values of the parameters be B1=1 , B2=1 . Let the true random error values, which are never known in reality, be ei= (1,-1,0,6,-6) . a) Calculate the values of yi b) Compute the OLS estimates of the parameter c) Compute the least squares residuals, e1 , e2 , e3 , e4 , e5 . What's their sum? d) It...
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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 =...
Consider the least-squares residuals ei-yi-yi, 1, 2, . . . , linear regression model. Find the variance of the residuals Var(e). Is the vari- ance of the residuals a constant? Discuss. n,from the simple
4. Consider the model yi-β +82i + ei. Find the OLS estimator for β.
3. Consider the linear model: Yİ , n where E(Ei)-0. Further α +Ari + Ei for i 1, assume that Σ.r.-0 and Σ r-n. (a) Show that the least square estimates (LSEs) of α and ß are given by à--Ỹ and (b) Show that the LSEs in (a) are unbiased. (c) Assume that E(e-σ2 Yi and E(49)-0 for all i where σ2 > 0. Show that V(β)--and (d) Use (b) and (c) above to show that the LSEs are consistent...
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