How to adjust this two series?

[quique3716]

Dear users,


I'm struggling with a problem of fitting two series of numbers (I'm using Excel). Let's go:


I have two series (A, B), consisting of several points recorded over time (a1, a2, a3...; b1, b2, b3...). Each series has different units (A="$", B="km"). I want to apply the formula (B'=mB+n) in order to have B' with the maximum possible correlation with A.


As an example:


A = (5,8,9,6,10,8 )
B = (4,5,6,5,7,5)
If m=2 and n=-3 then B'= (5,7,9,7,11,7)


Could you please explain to me to find the parameters "m" and "n" of the formula that give the maximum correlation?


Thank you in advance

 

[stapel]

I have two series (A, B), consisting of several points recorded over time (a1, a2, a3...; b1, b2, b3...). Each series has different units (A="$", B="km"). I want to apply the formula (B'=mB+n) in order to have B' with the maximum possible correlation with A.

As an example:

A = (5,8,9,6,10,8 )
B = (4,5,6,5,7,5)
If m=2 and n=-3 then B'= (5,7,9,7,11,7)

Could you please explain to me to find the parameters "m" and "n" of the formula that give the maximum correlation?

What, precisely, do you mean by "correlation" in this context?

When you reply, please also explain how the techniques of calculus are to be brought to bear, and provide a clear listing of your thoughts and efforts so far. Thank you!

 

[quique3716]

What, precisely, do you mean by "correlation" in this context?

Sorry, I didn't explain properly myself. What i want is to minimize the sum of squares in order to adjust B to A, applying the lineal formula (y=mx+n) to B. However, there's a condition: m must be higher than 1. According to the illustration:

(A: reference values; B: values to optimize; B': values after optimization using sum of squares; B'': something closer to what I expect, where m>1)

Many thanks