Question

Consider the linear regression model ? = ? +?? + ? Suppose the variance of e...

Consider the linear regression model ? = ? +?? + ? Suppose the variance of e increases as X increases. What implications, if any, does this have for the OLS estimators and how would you proceed to estimate β in this case.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose that your linear regression model includes a constant term, so that in the linear regression...
Suppose that your linear regression model includes a constant term, so that in the linear regression model Y = Xβ + ε The matrix of explanatory variables X can be partitioned as follows: X = [i X1]. The OLS estimator of β can thus be partitioned accordingly into b’ = [b0 b1’], where b0 is the OLS estimator of the constant term and b1 is the OLS estimator of the slope coefficients. a) Use partitioned regression to derive formulas for...
In the linear regression model ? = ?0 + ?1? + ?, let y be the...
In the linear regression model ? = ?0 + ?1? + ?, let y be the selling price of a house in dollars and x be its living area in square feet. Define a new variable ? ∗ = ? − 1000 (that is, ? ∗ is the square feet in excess of 1000), and estimate the model ? = ?0 ∗ + ?1 ∗? ∗ + ?. a] Show the relationship between the OLS estimators ?1̂∗ and ?̂1 ....
CW 2 List 5 assumptions of the simple linear regression model. You have estimated the following...
CW 2 List 5 assumptions of the simple linear regression model. You have estimated the following equation using OLS: ŷ = 33.75 + 1.45 MALE where y is annual income in thousands and MALE is an indicator variable such that it is 1 for males and 0 for females. a) According to this model, what is the average income for females? b) According to this model, what is the average income for females? c) What does OLS stand for? How...
Based on the definition of the linear regression model in its matrix form, i.e., y=Xβ+ε, the...
Based on the definition of the linear regression model in its matrix form, i.e., y=Xβ+ε, the assumption that ε~N(0,σ2I), and the general formula for the point estimators for the parameters of the model (b=XTX-1XTy); show: how to derivate the formula for the point estimators for the parameters of the models by means of the Least Square Estimation (LSE). [Hint: you must minimize ete] that the LSE estimator, i.e., b=XTX-1XTy, is unbiased. [Hint: E[b]=β]
Multiple Linear Regression We consider the misspecification problem in multiple linear regression. Suppose that the following...
Multiple Linear Regression We consider the misspecification problem in multiple linear regression. Suppose that the following model is adopted y = X1β1 + ε while the true model is y = X1β1 + X2β2 + ε. For both models, we assume E(ε) = 0 and V (ε) = σ^2I. Figure out conditions under which the least squares estimate we obtained is unbiased.
Consider the simple linear regression model and let e = y −y_hat, i = 1,...,n be...
Consider the simple linear regression model and let e = y −y_hat, i = 1,...,n be the least-squares residuals, where y_hat = β_hat + β_hat * x the fitted values. (a) Find the expected value of the residuals, E(ei). (b) Find the variance of the fitted values, V ar(y_hat ). (Hint: Remember that y_bar i and β1_hat are uncorrelated.)
Consider the simple linear regression model for which the population regression equation can be written in...
Consider the simple linear regression model for which the population regression equation can be written in conventional notation as: yi= Beta1(xi)+ Beta2(xi)(zi)2+ui Derive the Ordinary Least Squares estimator (OLS) of beta i.e(BETA)
Consider the multiple linear regression model y = β0 +β1x1 +β2x2 +β3x3 +β4x4 +ε Using the...
Consider the multiple linear regression model y = β0 +β1x1 +β2x2 +β3x3 +β4x4 +ε Using the procedure for testing a general linear hypothesis, show how to test a. H 0 : β 1 = β 2 = β 3 = β 4 = β b. H 0 : β 1 = β 2 , β 3 = β 4 c. H0: β1-2β2=4β3           β1+2β2=0
1. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this regression using OLS and...
1. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this regression using OLS and get the following results: b0=-3.13437; SE(b0)=0.959254; b1=1.46693; SE(b1)=21.0213; R-squared=0.130357; and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and b1, respectively. The total number of observations is 2950.According to these results the relationship between C and Y is: A. no relationship B. impossible to tell C. positive D. negative 2. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this...
Consider the simple linear regression model y=10+30x+e where the random error term is normally and independently...
Consider the simple linear regression model y=10+30x+e where the random error term is normally and independently distributed with mean zero and standard deviation 1. Do NOT use software. Generate a sample of eight observations, one each at the levels x= 10, 12, 14, 16, 18, 20, 22, and 24. Do NOT use software! (a) Fit the linear regression model by least squares and find the estimates of the slope and intercept. (b) Find the estimate of ?^2 . (c) Find...