*4.5. Multiple Linear Regression Model*

Relationships between the presence and level of microcystin and potential predictor variables were explored visually using plot functions and the strength of these relationships assessed using multiple linear regression models after making appropriate transformations data (if required) to ensure its distribution met the test assumptions. A logistic regression model (GLM assuming a binomial distribution and log link function) was also applied to determine whether any of the environmental variables measured were able to reliably predict the presence/absence of microcystin rather than its levels. For both the linear and logistic regression analysis, univariable analysis was first performed and then a multivariable model was built using a forward stepwise approach in which variables and combinations that led to statistically significantly reductions (*p* ≤ 0.05) in the Akaike information criteria (AIC) were retained in the model. The presence of two-way interaction effects was explored for all variable combinations but were only retained if their inclusion resulted in a significant reduction in AIC. All analysis and data visualisations were conducted in R version 4.0.2 [51].

**Author Contributions:** D.M.H., I.J.C., G.F.E., A.D.T., and D.J.F. designed and conceived the study, D.M.H., and I.J.C. performed the field and laboratory work, N.G.H.T. provided formal analysis G.F.E., D.J.F., and A.D.T. provided supervision, D.M.H. prepared the original draft, D.M.H., I.J.C., G.F.E., A.D.T., and D.J.F. reviewed the paper, and D.M.H. and N.G.H.T. wrote the revised drafts. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Bournemouth University post graduate studentships. Analytical chemical methods were funded by Cefas Seedcorn (Contract DP305).

**Acknowledgments:** The authors would like to thank Lewis Coates for preparing Figure 1, and Bournemouth Water, especially Ian Hayward the bailiff at Longham Lakes. D.M.H. would like to thank Rachel Hartnell for reviewing the original draft of this manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
