Statistical Tests: Probability of Randomly Distributed/ Constant Y-Values

[natski]

Hi everyone,

I can't remember which statistical tests are needed for the following two tests. I thought maybe the null hypothesis test but wanted to check on here first... Maybe something Bayesian?

Consider you have a plot of y against x with several data points on it, each with y error bars. I would like to calculate the probability that:

a) These points are randomly distributed

b) These points have the same y-value = constant, i.e. y is not a function of x.

Thanks for any advise.

Natski

 

[EnumaElish]

Describe "error bar."

For part b, my first approach would be to estimate the linear relationship y = a + b*x using least squares and show that b is not statistically significantly different from zero. But "y is not a function of x" is a very general statement; you may have to iterate with polynomial functions (of x), until you run out of data points.