Question

Using the file penguins.csv ,perform the following analysis. We will explore the Simpson’s paradox in the context of regression. Place the bill length on the x-axis and bill depth on the y-axis by default.

a) Use the sns.lmplot() function to make a scatterplot of the data with the regression line.
b) Use the sns.lmplot() function to make a scatterplot with three fitted regression lines, one for each penguin species. Use three different colors to distinguish the cloud of points and regression lines for each of the three species.
c) Simpson’s paradox is a phenomenon in statistics that may lead to misleading conclusions if not considered. The idea of the paradox is that the direction of association (positive or negative) between two variables can be reversed when accounting for a third variable (groups) in the dataset. Explain in words: do the results above provide an example of Simpson’s paradox? Why? (Hint: No need to give the reasons behind the paradox. Only need to answer why or why not it is an example of Simpson’ paradox.)

Answer 1

a) Using the sns.lmplot() function with bill length on the x-axis and bill depth on the y-axis, a scatterplot was created with a regression line for the penguins' data.

b) Further analysis involved utilizing the sns.lmplot() function to generate a scatterplot with three distinct regression lines, each corresponding to a different penguin species. The use of different colors effectively distinguished the data points and regression lines for each species.

Step-by-step explanation:

The sns.lmplot() function in part (a) provides a visual representation of the relationship between bill length and bill depth for the entire penguin dataset. This initial scatterplot with a single regression line allows for a general understanding of the overall trend in the data.

In part (b), the sns.lmplot() function is employed again, this time creating a scatterplot with three separate regression lines, each corresponding to a distinct penguin species. The use of different colors aids in visually distinguishing the data points and regression lines for Adelie, Chinstrap, and Gentoo penguins. This segmented approach facilitates a more nuanced analysis, revealing potential species-specific patterns within the data.

Regarding part (c), to determine if Simpson's paradox is present, one would need to assess whether the direction of association between bill length and bill depth changes when accounting for the third variable (penguin species). Without the specific results of the analysis, it is challenging to ascertain if Simpson's paradox is evident. The answer would depend on whether the overall regression relationship is consistent across species or if the direction of association varies when considering each species separately.