Math – Interpolation on Excel

35 40
-15 15.0 15.1
- 10 17.2 17.4
-5 19.7 19.8

z=A*x+B*y+C

I have this source data:

35 40
-15 15.0 15.1
-10 17.2 17.4
-5 19.7 19.8

I need to find (-16, 37). I have tried linear interpolation, but I can only use (x, y) to solve the problem. Can you help me?

Thank you very much,
Andrea

You can try to fit the plane to the data:

z=A*x+B*y+C

Then use least squares and 6 points (-15, 35, 15.0) to solve A, B ,C,…
Excel may be able to find the best value for you.

Edit

Here, I inserted your data (green cells) and used The solver tool builds the best linear model z = Ax By C. (x is 35, 40, y is -15, -10, -5). A, B, C are the blue cells on the left. Then pink The cell is Axe C, the red cell is (date model) ^ 2. The error is the sum of all these 6 red blood cells.

Then use the Solver tool (requires activation from the Excel option). Define the error cell For the goal (minimization), define A, B, C as variable units. It will find the best A, B, C values.

Then apply these values ​​to your request (x = 37 and y = -16), get the result 14.5.