# How to demonstrate two variables are orthogonal with respect to the output in a 3-D Python dataset?

I have a Python dataset with 300 samples and 3 columns: 2 independent integer variables X,Y and the dependent continuous variable F (output).

The X variable can only take 3 values, but Ycan take up to 1024 different values. Based on my sample, I want to demonstrate that if X=x0 minimizes the output for a given Y=yi, i.e. x0=argmin_x F(x,yi) so F(x0,yi)<F(x1,yi)<F(x2,yi), then F(x0,yj) < F(x1,yj) < F(x2,yj) for all y=yj values.

How could I do this? I was thinking in converting values into probabilities and run a hypothesis test, but I am not very sure what test to implement and how in Python. Thank you

You can do that quite easily with pandas or numpy libraries, programming every step precisely.

For instance: (pseudo code for 2 ordered values)

x0 = 100000
x1 = x0 + 1

for i in range(0,len(y)):
x_temp = F(x,  y[i])
if x0<x_temp and x0<x1:
x0=x_temp

if x0>x_temp:
x1 = x0
x0 = xtemp


If you want a more precise code, I recommend adding a small data sample to your question.