Question
Microplastics are found in almost all marine and fresh water environments, where they pose a potential risk to fish and crustaceans. Therefore, the effects of microplastics on aquatic organisms are currently the subject of intense research. Here we have a dataset containing 200 seawater samples collected at different sites around a bay in Sweden. The dataset is saved as Mplastics.csv. There are 5 variables included in the study:
• PE = polyethylene microplastics (µg/m3)
• PP = polypropylene microplastics (µg/m3)
• PS = polystyrene microplastics (µg/m3)
• temp = water temperature at each site (Celsius)
• larvae = number of fish larvae of a single species per 100 m3
(a) Use the R function pairs to plot the data. Summarise the information available from the plot.
NB: save Rfunctions.R (available from Topic 2 block) to your working directory.
(b) Fit a model of the form
Print the table of regression coefficients and write down the least squares regression equation.
(c) Which variables are significant predictors of fish larvae density in this model, at a 5%level? Write down and test appropriate hypotheses.
Now drop the non-significant terms and refit the model using only the explanatory variables that are significant. This is referred to as the final model.
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(d) Print the table of regression coefficients and write down the least squares regressionequation for the final model.
(e) Find and interpret the 95% confidence intervals for the regression coefficients in the finalmodel.
(f) Produce the diagnostic plots for the final model and explain what can be understoodfrom the plots.
(g) Using the final model, estimate mean fish larvae density and the 95% CI for the estimate when
• temperature = 17.5, PE = 300, PP = 50, PS= 80.5 and
• temperature = 20.5, PE = 300, PP = 50, PS= 80.5
NB: You may not need to include values for all 4 predictor variables, depending on your final model.
Comment on the reliability of these predictions.
Write a concise, informative conclusion based on your analysis and results.
