More than two explanatory variables

Intermediate Regression with statsmodels in Python

Maarten Van den Broeck

Content Developer at DataCamp

From last time

sns.scatterplot(x="length_cm", 
                y="height_cm",
                data=fish,
                hue="mass_g")

2D scatter plot, with mass colored to visualize a third numeric variable.

Intermediate Regression with statsmodels in Python

Faceting by species

grid = sns.FacetGrid(data=fish,

                     col="species",

                     hue="mass_g",
                     col_wrap=2,

                     palette="plasma")

grid.map(sns.scatterplot,
         "length_cm",
         "height_cm")

plt.show()

Scatter plot of fish height, length and mass, faceted by species. Brighter color means heavier fish.

Intermediate Regression with statsmodels in Python

Faceting by species

  • It's possible to use more than one categorical variable for faceting
  • Beware of faceting overuse
  • Plotting becomes harder with increasing number of variables

Scatter plot of fish height, length and mass, faceted by species. Brighter color means heavier fish.

Intermediate Regression with statsmodels in Python

Different levels of interaction

No interactions

ols("mass_g ~ length_cm + height_cm + species + 0", data=fish).fit()

two-way interactions between pairs of variables

ols(
  "mass_g ~ length_cm + height_cm + species +
  length_cm:height_cm + length_cm:species + height_cm:species + 0", data=fish).fit()

three-way interaction between all three variables

ols(
  "mass_g ~ length_cm + height_cm + species + 
  length_cm:height_cm + length_cm:species + height_cm:species + length_cm:height_cm:species + 0", data=fish).fit()
Intermediate Regression with statsmodels in Python

All the interactions

ols(
  "mass_g ~ length_cm + height_cm + species + 
  length_cm:height_cm + length_cm:species + height_cm:species + length_cm:height_cm:species + 0", 
  data=fish).fit()

same as

ols(
  "mass_g ~ length_cm * height_cm * species + 0", 
  data=fish).fit()
Intermediate Regression with statsmodels in Python

Only two-way interactions

ols(
  "mass_g ~ length_cm + height_cm + species + 
  length_cm:height_cm + length_cm:species + height_cm:species + 0", 
  data=fish).fit()

same as

ols(
  "mass_g ~ (length_cm + height_cm + species) ** 2 + 0", 
  data=fish).fit()
Intermediate Regression with statsmodels in Python

The prediction flow

mdl_mass_vs_all = ols(
  "mass_g ~ length_cm * height_cm * species + 0",
  data=fish).fit()

length_cm = np.arange(5, 61, 5)
height_cm = np.arange(2, 21, 2)
species = fish["species"].unique()

p = product(length_cm, height_cm, species)

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

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

print(prediction_data)

     length_cm  height_cm species       mass_g
0            5          2   Bream  -570.656437
1            5          2   Roach    31.449145
2            5          2   Perch    43.789984
3            5          2    Pike   271.270093
4            5          4   Bream  -451.127405
..         ...        ...     ...          ...
475         60         18    Pike  2690.346384
476         60         20   Bream  1531.618475
477         60         20   Roach  2621.797668
478         60         20   Perch  3041.931709
479         60         20    Pike  2926.352397

[480 rows x 4 columns]
Intermediate Regression with statsmodels in Python

Let's practice!

Intermediate Regression with statsmodels in Python

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