import numpy as np
import pandas as pd
import plotly.graph_objects as go
import plotly.express as px
import plotly.figure_factory as ff

Fitting Linear Models

In this notebook we briefly review the normal equations, introduce the scikit-learn framework, evaluation metrics, and describe methods to visualize model fit.

Toy Data set

To enable easy visualization of the model fitting process we will use a simple synthetic data set.

data = pd.read_csv("data/synthetic_data.csv")
data.head()

	X0	X1	Y
0	-1.254599	4.507143	0.669332
1	2.319939	0.986585	5.430523
2	-3.439814	-3.440055	7.640933
3	-4.419164	3.661761	-1.836007
4	1.011150	2.080726	6.148833

We can visualize the data in three dimensions:

data_scatter = go.Scatter3d(x=data["X0"], y=data["X1"], z=data["Y"], 
                            mode="markers",
                            marker=dict(size=2))
layout = dict(margin=dict(l=0, r=0, t=0, b=0), 
              height=600,
              scene = dict(xaxis_title='X0', yaxis_title='X1', zaxis_title='Y'))
go.Figure([data_scatter], layout)