A. A. Walters (auth.)'s An Introduction to Econometrics PDF

By A. A. Walters (auth.)

ISBN-10: 0333025679

ISBN-13: 9780333025673

ISBN-10: 1349152773

ISBN-13: 9781349152773

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Sample text

And it is well known that the sum of squares of deviations from the mean will give a lower value than the sum of squares of deviations from any other value. The sensible approach seems to be, therefore, to calculate i[(x1- ~) 2 + (xa- ~) 2] and use this as a measure of the variance. This will not have the downward bias associated with the former measure. Unfortunately, we often do not know the value of ~ and so this course is rarely open to one. (3-4) L (x-~)ll=n(x-~) 2 2 2 But and so L (x1 - ~)(x- ~) =n(x- ~~, L (x 1 -x) 2 =:L (x,-~)9-n(x-~ 2• The second term on the right-hand side is (n times) the square of the difference between the sample mean and the true mean.

But for large samples the distribution oft approximates to the normal - and this is, of course, the assumption t The nQtation li - €1 means that we take the absolute value by converting all negative values of (x - {) into positive ones. STATISTICAL INFERENCE 43 which was made in large sample-theory. The mean value of the sampling distribution oft is zero. This is simply another version of the result which we observed for large samples that, as we take repeated samples of a given size from a population, the average of these sample means is the value of the hypothetical or true mean.

One chance in 40. By most people's ideas one chance in forty denotes an unlikely event. a. we should say that the hypothesis is discredited. We should 'reject' the hypothesis. In one out offorty cases we should, of course, be wrong in making statements of this kind- since there is a 0·025 chance that values as low as this, or lower, will occur when the population average is £r,ooo. But we might be quite willing to accept this small chance of being wrong. g. o·o25) and this gives the borderline (£8oo) between rejecting the hypothesis and accepting it.

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An Introduction to Econometrics by A. A. Walters (auth.)

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