Show absence of prediction for one response variable and multiple predictors

Question

I have the following question concerning ecological statistics in a scientific study I am performing. I have measured the amount of copepods (little invertebrates) at different locations and at different times of the year together with other parameters from the water. Thus:

• I have one single responsible variable y (in this case the number of live copepods in $1m^3$ of water).

• I have multiple predictor variables $x_1$ to $x_i$ (in this case temperature, acidity, salinity, amount of ammonium in the water, phosphate).

• I have done this at five different locations and for ten different months of the year each time. For a total of 50 different y variables measured and 250 x variables measured.

My hypothesis is that the copepods do not react to any of these environmental factors and they thrive independently of temperature, acidity, etc.

I thus would like a test to demonstrate the lack of correlation or lack of prediction power of the x variables. But I'm not sure what to do. How would you proceed? How would you express the certainty that these x do not influence y?

Answer 1

Fit a mixed effect Poisson regression model. Fixed: $x_1$ to $x_i$ and month; random: location specific intercept. Of course, the response variable $Y$ is the number of live copepods in 1m$^3$ of water.

Statistical test is used to demonstrate that response variable $Y$ and covariate $x_i$ has relation. Here you want to see they has NO relation. Then presenting the confidence interval (CI) is better than presenting p value.