Consider the following data set:
Say graduation rates for a specific college's undergraduate program that are the following:
| Year | # of Graduates |
|---|---|
| Year 11 | 10,500 |
| Year 12 | 10,750 |
| Year 13 | 11,000 |
| Year 14 | 11,750 |
| Year 15 | 9,000 |
| Year 16 | 11,500 |
| Year 17 | 12,125 |
| Projected | # of Graduates |
| Year 18 | ? |
| Year 19 | ? |
| Year 20 | ? |
| Year 21 | ? |
| Year 22 | ? |
If I wanted to generate a data projection for the next five years using only these seven data points given; specifically, projecting Year 18 to Year 22 (five projected data points); what would be the mathematically correct way for choosing the weights to mathematically correctly generate these projected five data points?
Specifically, given the following mathematical formula for weighted average (${{x}_{w}}$) as the sum of the: products of weights ($w$) of values ($v$), divided by the sum of the weights, given as:
${{x}_{w}}={[(w_1)(v_1)+(w_2)(v_2)+(w_3)(v_3)+{\cdot}{\cdot}{\cdot}+(w_n)(v_n) ]/[(w_1)+(w_2)+(w_3)+{\cdot}{\cdot}{\cdot}+(w_n)]}$
Then how do you mathematically correctly determine the values of the weights?
Remark: I'm sure this has something to do with time scale duration between each of the data points in this set; which in this case are equal to one another at 1 year each (365 days); but I don't know how that yields the mathematically correct determination of the weights?
Any help on this would be appreciated, thanks in advance.
There is no "mathematically correct" way. This is not a matter of mathematics. It is a matter of what model you believe best captures reality. The model you choose is based on your belief about how reality works -- not on mathematics.