3.1.6.3. Analysis of Iris petal and sepal sizes

Illustrate an analysis on a real dataset:

• Visualizing the data to formulate intuitions

• Fitting of a linear model

• Hypothesis test of the effect of a categorical variable in the presence of a continuous confound

import matplotlib.pyplot as plt

import pandas
from pandas import plotting

from statsmodels.formula.api import ols

# Load the data
data = pandas.read_csv("iris.csv")

Plot a scatter matrix

# Express the names as categories
categories = pandas.Categorical(data["name"])

# The parameter 'c' is passed to plt.scatter and will control the color
plotting.scatter_matrix(data, c=categories.codes, marker="o")

fig = plt.gcf()
fig.suptitle("blue: setosa, green: versicolor, red: virginica", size=13)

Text(0.5, 0.98, 'blue: setosa, green: versicolor, red: virginica')

Statistical analysis

# Let us try to explain the sepal length as a function of the petal
# width and the category of iris

model = ols("sepal_width ~ name + petal_length", data).fit()
print(model.summary())

# Now formulate a "contrast", to test if the offset for versicolor and
# virginica are identical

print("Testing the difference between effect of versicolor and virginica")
print(model.f_test([0, 1, -1, 0]))
plt.show()

                            OLS Regression Results
==============================================================================
Dep. Variable:            sepal_width   R-squared:                       0.478
Model:                            OLS   Adj. R-squared:                  0.468
Method:                 Least Squares   F-statistic:                     44.63
Date:                Mon, 07 Oct 2024   Prob (F-statistic):           1.58e-20
Time:                        04:56:51   Log-Likelihood:                -38.185
No. Observations:                 150   AIC:                             84.37
Df Residuals:                     146   BIC:                             96.41
Df Model:                           3
Covariance Type:            nonrobust
======================================================================================
                         coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------
Intercept              2.9813      0.099     29.989      0.000       2.785       3.178
name[T.versicolor]    -1.4821      0.181     -8.190      0.000      -1.840      -1.124
name[T.virginica]     -1.6635      0.256     -6.502      0.000      -2.169      -1.158
petal_length           0.2983      0.061      4.920      0.000       0.178       0.418
==============================================================================
Omnibus:                        2.868   Durbin-Watson:                   1.753
Prob(Omnibus):                  0.238   Jarque-Bera (JB):                2.885
Skew:                          -0.082   Prob(JB):                        0.236
Kurtosis:                       3.659   Cond. No.                         54.0
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
Testing the difference between effect of versicolor and virginica
<F test: F=3.245335346574177, p=0.07369058781701142, df_denom=146, df_num=1>