I am trying to write a formula in excel for the following problem –
There are 2 scales, one from 85% – 93% & the other from 91%-94%
At 85% & 91% on 2 scales, the answer is 50%, similarly at 93% & 94% on 2 scales the answer is 71%.
I am not able to write a formula in a way that if the values on these scales lie in between these numbers i.e 86% & 92% respectively, I get one answer (assuming the increase is linear).
I can do it with only 1 scale. i.e if value is b/w 85%-93% at 94% on the other scale.
The formula for one scale is follows –
If(value < 93%),( value - 85%)/ (93% - 85%) * (71% - 58%) + 58%, NA
I need to write a formula in which if i have a value of 86% and 92% on the 2 scales, I get one value from the table.
By inspection the formula should be
where x is the value on the first scale and y is the value on the second scale.
If you look at either row, you can see that the result increases by 13% for a change in input of 8%, and if you look at either column you can see that the output increases by 8% for a change in input of 3%. That is starting from baseline of 50%.
If you wanted to do it more formally you could assume an equation of
and solve it for any three values in the table. If the fourth value was consistent (which it is), it means that the assumption of linearity is correct. Or you could do a multiple regression.