Instructions

0. Load the data and save your dataframe as parasites

1. Let’s start by examining the relationship between divergence_time and parsim.

   • Based on the goals of the analysis, what is the response variable?
   • Visualize the relationship between the two variables (remember to include axes and title.)
   • In one to two sentences, describe what you see.

2. Fit the linear regression model and display the results.

   • Write the regression equation.
   • Interpret the slope and the intercept in the context of the data.
   • Recreate the visualization from Exercise 1, this time adding a regression line to the visualization geom_smooth(method = "lm").
   • What do you notice about the prediction (regression) line that may be strange, particularly for very large divergence times?

⊕This is called a “logit” transformation and takes values between \((0, 1]\) and maps them to \((-\infty, + \infty)\) like we desire while preserving their order.

3. Since parsim takes values between 0 and 1, we want to transform this variable so that it can range between \((-\infty, + \infty)\). This will be better suited for fitting a regression model (and interpreting predicted values!)

• Create a new variable transformed_parsim that is calculated as log(parsim/(1-parsim)). Add this variable to your data frame.
• Then, visualize the relationship between divergence_time and transformed_parsim. Add a regression line to your visualization.
  
• Write a 1-2 sentence description of what you observe in the visualization.

4. Which variable is the strongest individual predictor of parasite similarity between species? To answer this question, begin by fitting a linear regression model to each pair of variables.

• divergence_time and transformed_parsim
• distance and transformed_parsim
• BMdiff and transformed_parsim
• precdiff and transformed_parsim

Do not report the model outputs in a tidy format but do save each one as dt_model, dist_model, BM_model and prec_model respectively.

Would it be useful to compare the slopes in each model to choose the variable that is the strongest predictor of parasite similarity? Why or why not?

5. To compare the explanatory power of each individual predictor, we will look at \(R^2\) between the models. \(R^2\) is a measure of how much of the variability in the response variable is explained by the model (we will talk more about \(R^2\) and the mathematics behind it in an upcoming lecture!).

As you may have guessed from the name \(R^2\) can be calculated by squaring the correlation (recall the correlation from Lab 01). The correlation \(r\) takes values -1 to 1, therefore, \(R^2\) takes values 0 to 1. Intuitively, if \(r = 1 \text{ or }-1\), then \(R^2 = 1\), indicating the model is a perfect fit for the data. If \(r \approx 0\) then \(R^2 \approx 0\), indicating the model is a very bad fit for the data.

You can calculate \(R^2\) using the glance function. For example, you can calculate \(R^2\) for dt_model using the code glance(dt_model)$r.squared.

• Calculate \(R^2\) for each model fit in the previous exercise.
• Which variable is the strongest predictor of parasite similarity? Briefly explain your choice.