[Solved] STAT210-410 Assessment2-Microplastics

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 (g/m³)
• PP = polypropylene microplastics (g/m³)
• PS = polystyrene microplastics (g/m³)
• temp = water temperature at each site (Celsius)
• larvae = number of fish larvae of a single species per 100 m³
• Use the R function pairs to plot the data. Summarise the information available from the plot. [15 marks]

NB: save Rfunctions.R (available from Topic 2 block) to your working directory.

• Fit a model of the form

Print the table of regression coefficients and write down the least squares regression equation.

• 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.

• Print the table of regression coefficients and write down the least squares regressionequation for the final model.

• Find and interpret the 95% confidence intervals for the regression coefficients in the finalmodel. [10 marks]
• Produce the diagnostic plots for the final model and explain what can be understoodfrom the plots. [10 marks]
• Using the final model, estimate mean fish larvae density and the 95% CI for the estimate when [15 marks]
  • 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.