variance is defined as the sum of the squares of the deviations of each member of a sample (group if you will) from the average, divided by the count of the sample less 1.
You use it in the first paragraph, possibly to mean the difference between year one and year 2. Did you really mean difference in income, year to year?
2) To your question. Perhaps what you want to do is to estimate the income for year 2, with a range, i.e.., a confidence interval, on that year 2 income. In this case, half the answer is already there. Year 2 income is expected to be 115. As for a confidence interval, we are told 'between 110 and 120.' typical (i.e., 'common') usage would make this about the 95% confidence interval, so we would jack the rough statement into the appearance of precision by saying,
"Year 2 income is expected to be 115, +/- 5 (95% CI)."
Warning!!!:: Common usage is _very_ sloppy. Most people with experience at estimating a number rarely remember the cases out beyond 2 sigma (95% CI), and often discount them as 'exceptions.' the restatement does not actually add information to the picture, despite any appearances. the range of 110 to 120 is still a quick estimate, unless the speaker has additional data not yet shared.
and how many economists and others who estimate $ go back and review their projections, with an eye toward improving accuracy or precision?
Eddy wrote:
Suppose A's income is 100 in the year 1, and his income is expected to be anywhere between 110 and 120 in the year 2. What would be aI fear you are working with 2 things that you mean by 'variances.' The change in the point estimate from year 1 to year 2 is a change in the income, perhaps an average change between pairs of years. You could call this a trend, in Excel-speak. the difference between 110 and 120 is a potential difference in the year 2 income.
reasonable estimate of A's (expected) income variance from year 1 to
year 2? (Hey, not a homework question.)
At first, I thought I would calculate the variance from the pair of numbers {100, 115} and take it as the income variance. (115 is the median of 110 and 120, and I take it as a "reasonable" approximation of the second year income.) However, I don't feel quite right about this.
I am now thinking of taking the variances from the pairs {100, 120} and {100, 110}, and then use the difference of the variances as my answer to the question. Intuitively, the variance of {100, 110} provides the lower bonds of A's income variance, and that of {100, 120} is the upper bound. However, I am still very doubtful.
Suppose you were to sample income changes from a multitude of 'alternate universes' which are very close to this case. The year 2 income would fall near 115, with most cases between 110 and 120.
Draw the picture of the data, see what that tells you.
Any suggestion of how to give a reasonable estimate of the income variance in the above case? (Assuming uniform distribution between 110 and 120 is acceptable, if this assumption would help.) Thanks in advance.
Cheers, Jay
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