Practice qn on multiple regression

[narayananvenkat]

David..

Here is a qn.

A regression equation with 4 independent variables is estimated using 20 data points. the R2 is .46. An anlysit is testing to see whether all of the coefficients are equal zero. The p-value for the test is:

a. lower than .25
b.between .05 and .10
c. between .025 and .05
d.greater than .10

Although I feel a bit intuitively c is the answer9right?) after mechanical calculation, am I right? Please help.
venkat

 

[narayananvenkat]

David..

One more query.

One of assumption of Linear regression is homoskedasticy in error term.

I also read that unconditional heteroskedasticiy among residual errors will not affect regression. What do we mean by that? This is an "exception" to exception?

venkat

 

[narayananvenkat]

David..

One more....

An analyst runs a regression on three independant variables. he discovers that p vlaues for each indepenent variable are relatively high. But F test has a very small p value. The analyst is puzzled like me how f test can be statistically significant when the individual independent variables are not significant.
What violation of regression analysis has occured?

venkat

 

[David Harper CFA FRM]

Hi venkat,

1. I input into this XLS, I get p value of about 4.3%
see: http://sheet.zoho.com/public/btzoho/0924-fdist
(I don't know how to inuit; without the F lookup, this would be a hard question, IMO)

2. I think it helps to keep in mind that OLS regression is a method to produce estimates (e.g., slope, intercept) from estimators (the "recipe" formulas). It's the common (best?) method because of the desirable *properties* of those estimators, if the assumptions are valid. As usual (e.g. CAPM), some assumptions can typically be bent while other will break the model. Gujarati is definitely in the camp that heteroskedasticy is not necessarily deadly; but technially, the violation of the assumption has implication on estimators. Spefically, from Gujarati:

"Heteroscedasticity does not destroy the unbiasedness and consistency properties of OLS estimators. But these estimators are no longer minimum variance or efficient. That is, they are not BLUE."

I am unsure why the term "unconditional" is used (I have not given this deep thought, so maybe i miss something) but i *think* homoskedasticity implies equivalently:
E(error^2) = constant
E(error^2 | explanatory variable) = constant
...so i think the unconditional is unnecessary ...

But in any case, I answerd this way to draw your attention to the properties of the estimators. On closer look, we are a long way from saying a regression works or does not; e.g., OLS is only one approach, within OLS, we can produce estimates that are more/less useful

3. This is a classic practical consequence of multicollinearity (see Gujurati chapter 12 for detail disucssion)

David