Making predictions with interactions

Intermediate Regression with statsmodels in Python

Maarten Van den Broeck

Content Developer at DataCamp

The model with the interaction

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

The prediction flow

from itertools import product

length_cm = np.arange(5, 61, 5)

species = fish["species"].unique()

p = product(length_cm, species)

explanatory_data = pd.DataFrame(p,
                                columns=["length_cm",
                                         "species"])

prediction_data = explanatory_data.assign(
 mass_g = mdl_mass_vs_both_inter.predict(explanatory_data))

print(prediction_data)

    length_cm species     mass_g
0           5   Bream  -762.5977
1           5   Roach  -212.7799
2           5   Perch  -424.6178
3           5    Pike -1274.8499
4          10   Bream  -489.8478
5          10   Roach   -96.1836
6          10   Perch  -230.0604
7          10    Pike -1008.8756
8          15   Bream  -217.0979
...
40         55   Bream  1964.9014
41         55   Roach   953.1833
42         55   Perch  1520.9556
43         55    Pike  1384.8933
44         60   Bream  2237.6513
45         60   Roach  1069.7796
46         60   Perch  1715.5129
47         60    Pike  1650.8677

Visualizing the predictions

sns.lmplot(x="length_cm",
           y="mass_g",
           data=fish,
           hue="species",
           ci=None)

sns.scatterplot(x="length_cm",
                y="mass_g",
                data=prediction_data,
                hue="species")

plt.show()

A scatter plot of fish length vs. mass, for each species separately.

Manually calculating the predictions

coeffs = 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

ic_bream, ic_perch, ic_pike, ic_roach,
slope_bream, slope_perch, slope_pike, slope_roach = coeffs

Manually calculating the predictions

conditions = [
    explanatory_data["species"] == "Bream",
    explanatory_data["species"] == "Perch",
    explanatory_data["species"] == "Pike",
    explanatory_data["species"] == "Roach"    
]


ic_choices = [ic_bream, ic_perch, ic_pike, ic_roach]

intercept = np.select(conditions, ic_choices)


slope_choices = [slope_bream, slope_perch, slope_pike, slope_roach]

slope = np.select(conditions, slope_choices)

Manually calculating the predictions

prediction_data = explanatory_data.assign(
 mass_g = intercept + slope * explanatory_data["length_cm"])

print(prediction_data)

    length_cm species     mass_g
0           5   Bream  -762.5977
1           5   Roach  -212.7799
2           5   Perch  -424.6178
3           5    Pike -1274.8499
4          10   Bream  -489.8478
5          10   Roach   -96.1836
...
43         55    Pike  1384.8933
44         60   Bream  2237.6513
45         60   Roach  1069.7796
46         60   Perch  1715.5129
47         60    Pike  1650.8677

prediction_data = explanatory_data.assign(
 mass_g = mdl_mass_vs_both_inter.predict(explanatory_data))

print(prediction_data)

    length_cm species     mass_g
0           5   Bream  -762.5977
1           5   Roach  -212.7799
2           5   Perch  -424.6178
3           5    Pike -1274.8499
4          10   Bream  -489.8478
5          10   Roach   -96.1836
...
43         55    Pike  1384.8933
44         60   Bream  2237.6513
45         60   Roach  1069.7796
46         60   Perch  1715.5129
47         60    Pike  1650.8677

Let's practice!

Intermediate Regression with statsmodels in Python