# Finding the function of a set of numbers

• Feb 25th 2011, 04:45 AM
iDeals
Finding the function of a set of numbers
Okay, let me preface this as this is my first post and this is not for assistance in a math class rather a question in analytics. I have a few sets of numbers and I'm trying to figure out the function of how x & y interact to give me say z. I know for at least half of my problem my good 'ole Ti-84 can solve it, its just been so long since I've used it that I can't remember how to do it. The latter problem has more variables so I'm not sure that the Ti-84 can help.

Part 1 - the ceiling.

X-----Y
_______
75----51
76----51
77----52
78----53
80----54
etc....

^The above I believe I can plug into the calculator and it will spit me out a formula for a "Best fit" which may or may not work, but it will be a step in the right direction.

Part 2 - Where to begin

Below the first two numbers interact in such a way that they equal the third number, AND at the same time the second set of numbers interact to give the sixth number. Any ideas how I would go about finding the equation that is true for these figures?

107300 212000 =17 U 267500 117700 =79
111800 212000 =19 U 267500 121750 =73
114020 212000 =22 U 267500 124110 =70
137702 212000 =29 U 267500 =67
• Feb 27th 2011, 05:40 AM
HallsofIvy
So you want a function f(x,y) such that f(107300, 212000)= 19, f(267500, 11700)= 79, etc.? (You seem to have droped a y value for the last one.)

Since you have 8 values, you can set up 8 equations and solve for 8 coefficients. I would try something like
[/tex]f(x,y)= A+ Bx+ Cy+ Dx^2+ Exy+ Fy^2+ Gx^3+ Hy^3[/tex]
Now putting those values in for x, y, and f(x,y) gives you 8 linear equations to solve for A, B, C, D, E, F, G, H.

(To have a general cubic in two variables,we should also include \$\displaystyle x^2y\$ and \$\displaystyle xy^2\$ but that would require two more data points. The "resticted" cubic given will fit those 8 points for some coefficients.)
• Feb 27th 2011, 12:50 PM
CaptainBlack
Quote:

Originally Posted by iDeals
Okay, let me preface this as this is my first post and this is not for assistance in a math class rather a question in analytics. I have a few sets of numbers and I'm trying to figure out the function of how x & y interact to give me say z. I know for at least half of my problem my good 'ole Ti-84 can solve it, its just been so long since I've used it that I can't remember how to do it. The latter problem has more variables so I'm not sure that the Ti-84 can help.

Part 1 - the ceiling.

X-----Y
_______
75----51
76----51
77----52
78----53
80----54
etc....

^The above I believe I can plug into the calculator and it will spit me out a formula for a "Best fit" which may or may not work, but it will be a step in the right direction.

Part 2 - Where to begin

Below the first two numbers interact in such a way that they equal the third number, AND at the same time the second set of numbers interact to give the sixth number. Any ideas how I would go about finding the equation that is true for these figures?

107300 212000 =17 U 267500 117700 =79
111800 212000 =19 U 267500 121750 =73
114020 212000 =22 U 267500 124110 =70
137702 212000 =29 U 267500 =67

In order to help we need more information, like what these numbers represent and is their some theory on what the relation should look like.

CB