One model with an interaction
Intermediate Regression with statsmodels in Python
Maarten Van den Broeck
Content Developer at DataCamp
What is an interaction?
In the fish dataset
- Different fish species have different mass to length ratios.
- The effect of length on the expected mass is different for different species.
More generally
The effect of one explanatory variable on the expected response changes depending on the value of another explanatory variable.
Specifying interactions
No interactions
response ~ explntry1 + explntry2
With interactions (implicit)
response_var ~ explntry1 * explntry2
With interactions (explicit)
response ~ explntry1 + explntry2 + explntry1:explntry2
No interactions
mass_g ~ length_cm + species
With interactions (implicit)
mass_g ~ length_cm * species
With interactions (explicit)
mass_g ~ length_cm + species + length_cm:species
Running the model
mdl_mass_vs_both = ols("mass_g ~ length_cm * species", data=fish).fit()
print(mdl_mass_vs_both.params)
Intercept -1035.3476
species[T.Perch] 416.1725
species[T.Pike] -505.4767
species[T.Roach] 705.9714
length_cm 54.5500
length_cm:species[T.Perch] -15.6385
length_cm:species[T.Pike] -1.3551
length_cm:species[T.Roach] -31.2307
Easier to understand coefficients
mdl_mass_vs_both_inter = ols("mass_g ~ species + species:length_cm + 0", data=fish).fit()
print(mdl_mass_vs_both_inter.params)
species[Bream] -1035.3476
species[Perch] -619.1751
species[Pike] -1540.8243
species[Roach] -329.3762
species[Bream]:length_cm 54.5500
species[Perch]:length_cm 38.9115
species[Pike]:length_cm 53.1949
species[Roach]:length_cm 23.3193
Familiar numbers
print(mdl_mass_vs_both_inter.params)
species[Bream] -1035.3476
species[Perch] -619.1751
species[Pike] -1540.8243
species[Roach] -329.3762
species[Bream]:length_cm 54.5500
species[Perch]:length_cm 38.9115
species[Pike]:length_cm 53.1949
species[Roach]:length_cm 23.3193
print(mdl_bream.params)
Intercept -1035.3476
length_cm 54.5500
Let's practice!
Intermediate Regression with statsmodels in Python
