%matplotlib inline
from IPython.core.interactiveshell import InteractiveShell
InteractiveShell.ast_node_interactivity = "all"

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

Exercise 1: Linear Regression with 1 variable

1.Plotting the data

data=pd.read_csv('ex1data1.txt',names=['Population','Profit'],header=None)
x=data.loc[:,'Population']
x
y=data.loc[:,'Profit']
fig=plt.figure()
axe=fig.add_axes([0.1,0.1,0.8,0.8])
axe.set_xlabel('Population')
axe.set_ylabel('Profits')
axe.set_title('the scatter of PP')
axe.scatter(x,y)
x1=x
y1=y
m=len(data)
x=pd.DataFrame(x)
x.insert(0,'Ones',1)
x

2.Gradient descent

def hypothe(x,theta):
    return x.dot(theta)

def cost(u,y):
    s=len(y)
    return 1/(2*s)*sum((u-y)*(u-y))

theta=np.zeros(2)
x
theta
iterations=1500
alpha=0.01
i=1
cost_com=np.empty(0)
while i<iterations:
    for j in range(len(theta)):
        theta[j]-=alpha*(hypothe(x,theta)-y).dot(x.iloc[:,j])/m
    cost_com=np.hstack((cost_com,cost(hypothe(x,theta),y)))
    i+=1
cost_com
theta

	Ones	Population
0	1	6.1101
1	1	5.5277
2	1	8.5186
3	1	7.0032
4	1	5.8598
...	...	...
92	1	5.8707
93	1	5.3054
94	1	8.2934
95	1	13.3940
96	1	5.4369

97 rows × 2 columns

3.Visualizing J

fig=plt.figure()
axe=fig.add_axes([0.1,0.1,1.,1.])
axe.set_title('Cost function')
axe.set_xlabel('the cost')
axe.set_ylabel('the time of iterations')
axe.plot(cost_com)

cost(hypothe(x,theta),y)

4.483134519095647

tx=np.vstack((np.ones(1000),np.linspace(5,30,1000))).T
fig=plt.figure()
axe=fig.add_axes([0.1,0.1,1.,1.])
axe.set_title('the Result of Linear Regression')
axe.set_xlabel('the population')
axe.set_ylabel('the porfit')
axe.plot(np.linspace(5,30,1000),tx.dot(theta),'r')
axe.scatter(x1,y1)

Exercise 2: Linear Regression with multiple variables

1.Feature normalization

data=pd.read_csv('ex1data2.txt',names=['sizes','bedrooms','price'],header=None)
data.head()
data.describe()
mean_std=pd.DataFrame([],columns=['mean','std'],index=['sizes','bedrooms'])
for i in range(2):
    mean_std.iloc[i,:]=[data.iloc[:,i].mean(),data.iloc[:,i].std()]
    data.iloc[:,i]=(data.iloc[:,i]-data.iloc[:,i].mean())/data.iloc[:,i].std()
mean_std
m=len(X)

	sizes	bedrooms	price
0	2104	3	399900
1	1600	3	329900
2	2400	3	369000
3	1416	2	232000
4	3000	4	539900

	sizes	bedrooms	price
count	47.000000	47.000000	47.000000
mean	2000.680851	3.170213	340412.659574
std	794.702354	0.760982	125039.899586
min	852.000000	1.000000	169900.000000
25%	1432.000000	3.000000	249900.000000
50%	1888.000000	3.000000	299900.000000
75%	2269.000000	4.000000	384450.000000
max	4478.000000	5.000000	699900.000000

	mean	std
sizes	2000.68	794.702
bedrooms	3.17021	0.760982

X=np.hstack((np.ones((m,1)),data.iloc[:,:-1]))
y=data.iloc[:,-1]
theta=np.zeros(3)
n=len(theta)

def hypothe_multi(theta,X):
    return X.dot(theta)

def cost_multi(theta,X,y):
    s=len(y)
    return 1/(2*s)*(X.dot(theta)-y).dot(X.dot(theta)-y)

iterations=1500
alpha=0.01
i=1
cost_com_multi=np.empty(0)
while i<iterations:
    for j in range(n):
        theta[j]-=alpha*(hypothe_multi(theta,X)-y).dot(X[:,j])/m
    cost_com_multi=np.hstack((cost_com_multi,cost_multi(theta,X,y)))
    i=i+1
fig=plt.figure()
axe=fig.add_axes([0.1,0.1,0.8,0.8])
axe.set_xlabel('the cost')
axe.set_ylabel('the time of iterations')
axe.set_title('the multi-variable linear regression')
axe.plot(cost_com_multi)

theta

array([340412.56203904, 110541.98853995,  -6560.60505947])