# How to extract a a set of values from a range of indexes

Hi everyone I'm having some difficulty with a "chaining indexes" question I've come across in my statistics module and was wondering if anyone could help?

I've worked out q1) and q2) and need help with q3) or any pointer in the right direction.

An insurance company uses a index to describe the number of agents working for it. Starting ten years ago, the index (index 1) takes the values 110, 125, 142, 167, 185, 207 (for consecutive years. The index is then re-based so that the value of the new index is 100 in the same in the year that the old index is 207. The new index (index 2) then takes the values 95, 97, 83, 76 for the next four consecutive years.

1) If the company had not changed to index 2, what values would index 1 have in years 7-10

2) What values would index 2 have in years 1-5?

3) If the company had 486 agents in year 8, how many did it have in each of the other years?

I have answered question 1) and 2) here. Would appreciate any help in q3).

Many thanks in advance!

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This question has nothing to do with statistics, I am afraid. – Sasha Oct 27 '11 at 16:37

## 1 Answer

Your answers to questions 1) and 2) look OK.

There's a linear relationship between the index $x$ and the number $y$ of agents: $y=\lambda x$. You've got one pair of values, say, if you use index 2: $x=87$, $y=486$. So $486=87\lambda$, so $\lambda=486/87$. Now you can use $y=\lambda x=(486/87) x$ to fill in the remaining numbers of agents.

Less formally speaking, these are all just different scales for the same numbers, and you can get any of the columns by scaling any of the others by an appropriate factor; if you have one value in any of the columns, you can use that to find the scaling factor between that and one of the known columns, and scale the rest of that known column accordingly.

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Thanks for the help! It works fantastically! – methuselah Oct 29 '11 at 9:54