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deriving properties of the OLS estimator

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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)

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Solution Summary

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

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