Models for each category

Intermediate Regression with statsmodels in Python

Maarten Van den Broeck

Content Developer at DataCamp

Four categories

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

array(['Bream', 'Roach', 'Perch', 'Pike'], dtype=object)

Splitting the dataset

bream = fish[fish["species"] == "Bream"]
perch = fish[fish["species"] == "Perch"]
pike = fish[fish["species"] == "Pike"]
roach = fish[fish["species"] == "Roach"]

Four models

mdl_bream = ols("mass_g ~ length_cm", data=bream).fit()
print(mdl_bream.params)

Intercept   -1035.3476
length_cm      54.5500

mdl_perch = ols("mass_g ~ length_cm", data=perch).fit()
print(mdl_perch.params)

Intercept   -619.1751
length_cm     38.9115

mdl_pike = ols("mass_g ~ length_cm", data=pike).fit()
print(mdl_pike.params)

Intercept   -1540.8243
length_cm      53.1949

mdl_roach = ols("mass_g ~ length_cm", data=roach).fit()
print(mdl_roach.params)

Intercept   -329.3762
length_cm     23.3193

Explanatory data

explanatory_data = pd.DataFrame(
    {"length_cm": np.arange(5, 61, 5)})

print(explanatory_data)

    length_cm
0           5
1          10
2          15
3          20
4          25
5          30
6          35
7          40
8          45
9          50
10         55
11         60

Making predictions

prediction_data_bream = explanatory_data.assign(

    mass_g = mdl_bream.predict(explanatory_data),

    species = "Bream")

prediction_data_perch = explanatory_data.assign(

    mass_g = mdl_perch.predict(explanatory_data),

    species = "Perch")

prediction_data_pike = explanatory_data.assign(

    mass_g = mdl_pike.predict(explanatory_data),

    species = "Pike")

prediction_data_roach = explanatory_data.assign(

    mass_g = mdl_roach.predict(explanatory_data),

    species = "Roach")

Concatenating predictions

prediction_data = pd.concat([prediction_data_bream,
                             prediction_data_roach,
                             prediction_data_perch,
                             prediction_data_pike])

    length_cm       mass_g species
0           5  -762.597660   Bream
1          10  -489.847756   Bream
2          15  -217.097851   Bream
3          20    55.652054   Bream
4          25   328.401958   Bream
5          30   601.151863   Bream
...
3          20  -476.926955    Pike
4          25  -210.952626    Pike
5          30    55.021703    Pike
6          35   320.996032    Pike
7          40   586.970362    Pike
8          45   852.944691    Pike
9          50  1118.919020    Pike
10         55  1384.893349    Pike
11         60  1650.867679    Pike

Visualizing predictions

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

plt.show()

A scatter plot of fish length vs. mass, for each species separately. The slopes are not parallel anymore

Adding in your 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",
                ci=None,
                legend=False)

plt.show()

scatter-fish-mass-vs-length-by-species-inter-with-preds.png

Coefficient of determination

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

print(mdl_fish.rsquared_adj)

0.917

print(mdl_bream.rsquared_adj)

0.874

print(mdl_perch.rsquared_adj)

0.917

print(mdl_pike.rsquared_adj)

0.941

print(mdl_roach.rsquared_adj)

0.815

Residual standard error

print(np.sqrt(mdl_fish.mse_resid))

print(np.sqrt(mdl_bream.mse_resid))

74.2

print(np.sqrt(mdl_perch.mse_resid))

print(np.sqrt(mdl_pike.mse_resid))

print(np.sqrt(mdl_roach.mse_resid))

38.2

Let's practice!

Intermediate Regression with statsmodels in Python