Purchase Solution

deriving properties of the OLS estimator

Not what you're looking for?

Ask Custom Question

Inferences in Regressin and Corelation Analysis.

Please make sure not to jump in big steps, I need to know how to solve these, thanks, It would be nice if you would give some explanation to your steps when you solve these.

1. Derive the property in for the ki.
2. Show that bo as defined in is an unbiased estimator of βo.
3. Derive the expression in for the variance of bo, making use of . Also explain how variance is a special case of variance .
4. Suppose that normal error regression model , is applicable except that the error variance is not constant; rather the variance is larger, the larger X is. Does still imply that there is no linear association between X and Y? That there is no association between X and Y? Explain. (This is written like this in the book, looks like repetitive to me)

Attachments
Purchase this Solution
Solution Summary

The following shows a derivation of several aspects of the OLS slope estimator. Topics include bias, variance, heteroscedasticity.

Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

View More Free Quizzes
Related BrainMass Solutions

  • central limit theorem

    standard normal distribution. 2) b) the OLS estimator is biased.

  • Asymptotic Variance under multiple regression

    Indeed, the IV estimator is simply a special case (a generalization, really) of the 2SLS estimator (and OLS is a special case of IV estimation and GMM is a special case of 2SLS). I refer you to the attached file from Prof.

  • Heteroskedasticity

    Estimator B*=[Σ(PCON/REG)(X/REG)]/[Σ(X/REG)^2] So, B* is also unbiased and more efficient. And WLS estimator is the ratio of the means.

  • Matrix Algebra

    = b (say), (on simplification) The above expression of , (say) b is the estimate of Using OLS, the estimate of is given by, denoted as b, Here X'X = = 4 +16 + 36 + 64 + 100 = 220 X'Y = = 2 + 8 + 18 + 24 +

  • Statistical Inference(Maximum Likelihood Estimator for CDF)

    The solution illustrates the determination of method of moment estimator and maximum likelihood estimator for the parameter of distribution in step-by-step calculations. The properties of the estimator are also discussed thoroughly.

  • Residual Plot in Regression: Homoskedasticity v. Heteroskedasticity

    Var(ut)= σ2 Zi2 The consequence of heteroskedasticity is that ordinary lest square (OLS) estimators are still linear and unbiased but it may not be the best estimator (i.e inefficient).

  • Multicollinearity in Your Regression Model

    OLS is no longer the minimum-variance estimator. b. If you have a small number of observations (50), it is still possible that you will obtain statistically significant estimates of β2 and β3. c.

  • Observed Random Process

    (b) Analyze the convergence properties of your adaptive estimator. The explanations are in the attached file.

  • Setting up likelihood function and finding MLE

    It involves finding the likelihood of any sequence of s trials, finding maximum likelihood estimator of theta, and finding the expression of a posterior.

View More Related Solutions