Model Optimization

Introduction to Linear Modeling in Python

Jason Vestuto

Data Scientist

Residuals

2 panel figure, top plot scatter of sea level versus time and line plot of model, then bottom plot of residuals, showing difference between data and model from the top plot

residuals = y_model - y_data
len(residuals) == len(y_data)

True

Residuals Summed

2 panel figure, top plot scatter of sea level versus time and line plot of model, then bottom plot of residuals, showing difference between data and model from the top plot

residuals = y_model - y_data
print(np.sum(residuals))

0.0

Residuals Squared

2 panel figure, top plot scatter of sea level versus time and line plot of a poor model of constant value, then bottom plot of residuals as green dot markers and squared residuals as blue square markers

residuals_squared = np.square(y_model - y_data)

print(np.sum(residuals_squared))

65.1

RSS

resid_squared = np.square(y_model - y_data)
RSS = np.sum(resid_squared)

RSS

2 panel figure, top plot scatter of sea level versus time and line plot of a better model, then bottom plot of residuals as green dot markers and squared residuals as blue square markers, but with a much better fit

RSS = np.sum(np.square(y_model - y_data))
print(RSS)

5.9

Variation of RSS

Plot of RSS y-axis values versus slope x-axis values, shaped as an up-turned parabola or well, with minimum at the bottom near slope=25

Minimum value of RSS gives minimum residuals
Minimum residuals give the best model

Let's practice!

Introduction to Linear Modeling in Python