Linear Relationships¶

Exercise 1: Causation¶

Take a look at the website Spurious Correlations

How do you think was the website created?

Exercise 2: Scatter Plot¶

Draw a scatter plot of the penguins in penguins.csv. Plot the flipper length vs the body mass of all penguins.

In Python, you can use the following code:

import seaborn as sns

df = sns.load_dataset('penguins')
sns.scatterplot(data=df, x="...", y="...")

Exercise 3: Linear Regression¶

Fit a straight line into the data (also called Ordinary Least Squares).

In Python, a quality library for OLS models is statsmodels. Use the following code:

from statsmodels.regression.linear_model import OLS
from statsmodels import api as sm

df = df.dropna(inplace=True)
X = df[...]
X = sm.add_constant(X)
y = df[...]

model = OLS(y, X).fit()
model.summary()

Discuss the meaning of some elements in the output.

Exercise 4: Draw the line of fit¶

Calculate a line of best fit between a minimum and maximum x value:

xpred = [..., ...]
xpred = sm.add_constant(xpred)
ypred = model.predict(xpred)

Inspect the values, then plot the line:

sns.scatterplot(data=df, x='flipper_length_mm', y='body_mass_g')
plt.plot(x, yline, color="red")

Exercise 5: Error¶

Write code to calculate the mean squared error (MSE) for the penguins:

ypred = model.predict(X)
diff = y - ypred
...

Exercise 6: Anscombes Quartet¶

Examine the Anscombe Quartet data. It is an artificial dataset consisting of four separate groups. Start by examining the mean and standard deviation of each group:

a = sns.load_dataset('anscombe')

a.groupby('dataset').agg(['mean', 'std'])

Consider creating a linear fit for each of these groups. What would you have to take into account?

Exercise 7: Correlations¶

Play a few rounds of Guess the Correlation

Exercise 8: Correlation Coefficients¶

Calculate the correlation coefficients of the penguin dataset:

df.corr()

Exercise 9: Heatmap¶

Plot the correlation coefficients as a heatmap:

sns.heatmap(df.corr(), annot=True)

Exercise 10: Add Categories¶

Add extra columns for the species, converting them to integer columns. This is called dummy encoding or one-hot-encoding:

import pandas as pd

binary = pd.get_dummies(df['species'])
df2 = pd.concat([df, binary], axis=1)

Calculate correlation coefficients for the new columns as well.

Exercise 11: Scatterplot Matrix¶

Here is a particularly useful way to examine pairs of variables:

sns.pairplot(df, hue="species")

Exercise 12: Confounding Factors¶

Examine the relationship of beak length vs beak depth. Could you construct a linear model for these as well?