如何通过替换theta 0和theta 1的值使用假设函数在图形上进行绘制

Question

这是假设函数h（x）= theta 0 + theta 1（x）将theta 0的值设为0并将theta 1的值设为0.5之后，如何将其绘制在图形上？

Answer 1

It is the same way that we graph the linear equations. Let us assume h(x) as y and θ as some constant and x as x. So we basically have a linear expression like this y = m + p * x (m,p are constants) . To even simplify it assume the function as y = 2 + 4x. To plot this we will just assume the values of x from a range (0,5) so now for each value of x we will have corresponding value of x. so our (x,y) set will look like this ([0, 1, 2, 3, 4], [2, 6, 10, 14, 18]). Now the graph can be plotted as we know both x and y coords.

Answer 2

You simply plot the line equation y = 0 + 0.5 * x

So you get something like this plot

Here's how I did it with Python

import matplotlib.pyplot as plt
import numpy as np

theta_0 = 0
theta_1 = 0.5

def h(x):
    return theta_0 + theta_1 * x

x = range(-100, 100)
y = map(h, x)

plt.plot(x, y)
plt.ylabel(r'$h_\theta(x)$')
plt.xlabel(r'$x$')
plt.title(r'Plot of $h_\theta(x) = \theta_0 + \theta_1 \cdot \ x$')
plt.text(60, .025, r'$\theta_0=0,\ \theta_1=0.5$')

plt.show()