# Show absence of prediction for one response variable and multiple predictors

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?

• What is the typical number of live copepods in 1m3 of water? How are you counting them? Commented Oct 13, 2018 at 3:56

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.