Hello, Could you please assist in understanding of the regression assumption. Assumption #4. The variance of the error term is the same for all observations: E(sqr(ei)) = VARIANCE(e). Interpreting the formula, the expected value of the squared term is equal to the variance of the error term. But the assumption #3 says that the expected value of every single error term is 0, thus the variance of the error term should be also zero. Assumption #5 The error term, e, is uncorrelated across observations. How can we compute correlation between only two values? The assumption says that E(ei ej) =0. To me this means that we can take any couple of error terms and their correlation is expected to be zero? Doesn’t make sense.
assumption 4 - the part you wrote isn’t what the math equation states?.. the expected value of the error term square is equaled to the variance which is constant…key importance here is ‘homoscedasticity’… in other words, no heteroscedasticity (varying variances)…homoscedasticity is 'CONSTANT VARIANCES OF THE ERRORS. assumption 5 - this states there is no auto-correlation… i.e., the error term in period i is not correlated with period j… be careful in not interpreting this as anything but the ERROR terms not being serially correlated. In other words, no positive or negative auto-correlation (serial correlation)…key here is errors are independentt of each other across periods this is all from the top of my head from last exam in June so I don’t know if it’s perfectly accurate but just thought I’d help since I don’t think you are getting what the assumtions are stating to begin with… This section is a difficult one for most, so good call on starting early with quantitative methods section!! let me know if this makes sense to you… hope it helped
one more thing: make sure you understand the assumptions very well…because you need to know how to detect and correct for them too (and this would be very difficult if you don’t have a solid grasp of the fundamentals) like with the homoscedasticity…when you get into the ARCH model later in this subject, you really need to understand this stuff…for example, stock market data often has varying volatility over time, and the ARCH model deals with this (in an auto-regressive model) hope this helps/makes sense at all
Thanks Wannabe, it makes sense. Thus, the assumption #4 states that the expected value of the error term is constant and equal to the variation. The assumption #5 states that there is no correlation between the error terms of two different samples. I have one more question regarding the regression tables. In all examples in the book, Standard Error is always given along with the regression coefficients, for instance p316, R11. I understand how the coefficients are calculated, but not sure were the standard errors (not the standard error of estimate) come from.
See this for computing standard error. Enjoy it while it lasts. http://www.nd.edu/~rwilliam/stats1/x91.pdf
kyrylo Wrote: ------------------------------------------------------- > Thanks Wannabe, it makes sense. Thus, the > assumption #4 states that the expected value of > the error term is constant and equal to the > variation. The assumption #5 states that there is > no correlation between the error terms of two > different samples. > > I have one more question regarding the regression > tables. In all examples in the book, Standard > Error is always given along with the regression > coefficients, for instance p316, R11. I understand > how the coefficients are calculated, but not sure > were the standard errors (not the standard error > of estimate) come from. no…closer though. Very importantly, variation does not equal variance…i think it should read: the expected value of the squared error term i is equal to the variance. Not variance i…because it’s homoscedastic - constant variance. again with 5, no…auto (serial) correlation is normally present in Time Series data…and yeah, it means the error term in period i should not be dependent on the error term in period j (simply put, two different periods, not just samples) just off the top of my head, I’m fairly positive you aren’t required to compute standard error…but i dont know, check the LOS for that. Hope this helps:) keep the questions coming…glad to help
Thanks again. This clarifies the subject.