linear regression: my plotting doesn't show the line

Question

I am working on implementing from scratch a linear regression model means without using Sklearn package.

all was working just fine , until i tried ploting the result.

my fit line isn't showing:

i looked at a bunch of solution but neither of them was for myy problem

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import warnings

warnings.filterwarnings('ignore')
data = pd.read_csv(r'C:\Salary.csv')

x=data['Salary']

y=data['YearsExperience']


#y= mx+b

m = 0
b = 0

Learning_Rate = .01
epochs = 5000

n = np.float(x.shape[0])
error = []

for i in range(epochs):
   Y_hat = m*x+b

#error
   mse= (1/n)*np.sum((y-Y_hat)**2)
   error.append(mse)

#gradient descend
   db = (-2/n) * np.sum(x*(y-Y_hat))
   dm = (-2/n) * np.sum((y-Y_hat))

   m = m - Learning_Rate * dm
   b = b - Learning_Rate * db

#tracing x and y line
x_line = np.linspace(0, 15, 100)
y_line = (m*x_line)+ b



#ploting result
plt.figure(figsize=(8,6))

plt.title('LR result')
**plt.plot(x_line,y_line) #the problem is apparently here
                        # i just don't know what to do**
plt.scatter(x,y)
plt.show()

appart from that, there is no problem with the code .

Answer 1

Your code has multiple problems:

• you are plotting the line from 0 and 15, while data range from about 40000 to 140000. Even if you are correctly computing the line, you are going to plot it in a region far away from your data

• in the loop there is a mistake in the computation of dm and db, they are swapped. The corrected expressions are:

  dm = (-2/n)*np.sum(x*(y - Y_hat))
  db = (-2/n)*np.sum((y - Y_hat))
  

• your x and y data are on very different scales: x is ~10⁴ magnitude, while y is ~10¹. For this reason, also m and b will likely be very different from each other (different orders of magnitude). This is the reason why you should use two different learning rate for the different quantities you are optimizing: Learning_Rate_m for m and Learning_Rate_b for b

• finally, the gradient descent method is strongly affected by the initial guess: it may lead to find local minima (fake solutions) in place of the global minima (true solution). For this reason, you should try with different initial guesses for m and b, possibly close to their estimated value:

  m = 0
  b = -2
  

Complete Code

import numpy as np
import matplotlib.pyplot as plt


N = 40
np.random.seed(42)
x = np.random.randint(low = 38000, high = 145000, size = N)
y = (13 - 1)/(140000 - 40000)*(x - 40000) + 1 + 0.5*np.random.randn(N)


# initial guess
m = 0
b = -2

Learning_Rate_m = 1e-10
Learning_Rate_b = 1e-2
epochs = 5000

n = np.float(x.shape[0])
error = []


for i in range(epochs):
   Y_hat = m*x + b

   mse = 1/n*np.sum((y - Y_hat)**2)
   error.append(mse)

   dm = -2/n*np.sum(x*(y - Y_hat))
   db = -2/n*np.sum((y - Y_hat))

   m = m - Learning_Rate_m*dm
   b = b - Learning_Rate_b*db


x_line = np.linspace(x.min(), x.max(), 100)
y_line = (m*x_line) + b


plt.figure(figsize=(8,6))

plt.title('LR result')
plt.plot(x_line,y_line, 'red')

plt.scatter(x,y)
plt.show()

Plot