What makes a model linear

Introduzione alla modellazione lineare in Python

Jason Vestuto

Data Scientist

Taylor Series

Things to know:

approximate any curve
polynomial form: y = a0 + a1*x + a2*x**2 + a3*x**3 + .... + an*x**n
often, first order is enough: y = a0 + a1*x

Series Terms: a0=1

Plot of a constant y=1 line with slope zero

Series Terms: a1=1

Plot of line with nonzero slope y = 1*x

Series Terms: a2=1

Plot of quadratic line y = x^2, half a parabola, up turned

Combining all Terms

Plot of 4 curves, y=1 in red, y=x in green, y=x^2 in blue, and the sum of those three, in black

Real Data

Scatter plot of sea level change versus time in years

Zeroth Order

Scatter plot of data, sea level versus time, and line plot of model y=6.5, the mean of the data

First Order

Scatter plot of data, sea level versus time, and line plot of model y=5 + 0.08*x, with the model line passing through most data points

Higher Order

Scatter plot of data, sea level versus time, and line plot of model y=5 + 0.08*x + 0.0025*x^2, with the model line fitting data points

Over-fitting

Scatter plot of data sea level versus time, twice as far in time, with 2 models, line plot y=6.5 + 0.08x fitting data well, and line plot of model y=5 + 0.08*x + 0.0025*x^2, deviating strongly at later times

Let's practice!

Introduzione alla modellazione lineare in Python