Perfecting Models with Error Minimization

import numpy as np 
import pandas as pd
import matplotlib.pyplot as plt
df=pd.read_csv("old_faithful.csv")
df

	eruptions	waiting
0	3.600	79
1	1.800	54
2	3.333	74
3	2.283	62
4	4.533	85
...	...	...
267	4.117	81
268	2.150	46
269	4.417	90
270	1.817	46
271	4.467	74

272 rows × 2 columns

Plotting data

fig,ax1=plt.subplots()
ax1.scatter(df['eruptions'], df['waiting'])
ax1.set_xlabel('eruption time')
ax1.set_ylabel('waiting time')

Text(0, 0.5, 'waiting time')

Visualize the raw error

model=np.empty(2)
#guess slope
model[0]=20
#guess intercept
model[1]=10

def plot_raw_error(xdata, ydata, model):
    fig,ax2=plt.subplots()
    
    #plot raw data points
    ax2.scatter(xdata, ydata)

    #get model y data
    model_ydata=xdata*model[0] + model[1]

    #plot best fit line
    ax2.plot(xdata, model_ydata)

    #calculate error values
    raw_error_values=ydata-model_ydata
    plt.plot([xdata,xdata], [ydata,ydata-raw_error_values], 'c')

plot_raw_error(df['eruptions'], df['waiting'], model)

Calculate root mean square error

xdata=df['eruptions']
ydata=df['waiting']

def calc_rms_error(model):
    model_ydata=xdata*model[0] + model[1]
    raw_error_values=ydata-model_ydata
    rms_error=np.sqrt(np.mean(raw_error_values**2))
    return rms_error

calc_rms_error(model)

14.991246220221123

Optimizing RMS error

import scipy.optimize as opt
model_fit=opt.minimize(calc_rms_error, [15,20])
model_fit['x']

array([10.72963549, 33.47440846])

plot_raw_error(xdata, ydata, model_fit['x'])

Prediction using optimized model

# Waiting time for an eruption when eruption time is 6
eruption_time=6
waiting=model_fit['x'][0]*eruption_time + model_fit['x'][1]
waiting

97.85222136878929