

In [13]:

    
import pandas as pd
import numpy as np
from sklearn import linear_model, datasets
from sklearn.model_selection import train_test_split

import matplotlib.pyplot as plt
%matplotlib inline

Linear Regression refresher

Some random data



In [28]:

    
y = np.array([0.72*i*np.random.randint(1,20) + 2*i for i in range(50)])
x = np.array([i for i in range(len(y))])
plt.scatter(x,y);

Now to Linear Regret it.



In [29]:

    
from sklearn.linear_model import LinearRegression
a = LinearRegression()

#putting the input data into a df to feed to the LM model as it doesn't like 1d arrays
df = pd.DataFrame(x, columns=['Input'])
df.head()



In [30]:

    
a.fit(df, y)
plt.scatter(x,y, label='Original Data')
plt.plot(a.predict(df), color='r', label='Predictions')
plt.legend();

Split your data set into testing and training:



In [40]:

    
x_train, x_test, y_train, y_test = train_test_split(df,y)
len(x_train), len(x_test), len(y_train), len(y_test)









    Out[40]:





(37, 13, 37, 13)

Here we can see the model does a relatively good job of predicting the data it was trained on:



In [48]:

    
a2 = LinearRegression()
a2.fit(x_train,y_train)
a2.predict(x_test)

#plt.scatter(x,y, label='Original Data')
plt.plot(a2.predict(x_train), color='r', label='Predictions')
plt.plot(y_train, label="Actual", color="b")
plt.legend();

But it doesn't do a good job on the test data:



In [49]:

    
#plt.scatter(x,y, label='Original Data')
plt.plot(a2.predict(x_test), color='r', label='Predictions')
plt.plot(y_test, label="Actual", color="b")
plt.legend();

Another data set



In [10]:

    
boston = datasets.load_boston()
data = pd.DataFrame(boston.data)
data.head()



In [11]:

    
target = boston.target
target.shape









    Out[11]:





(506,)



In [12]:

    
lm = LinearRegression()
lm.fit(data, target)
predicted = lm.predict(data)
plt.plot(predicted, label='predicted')
plt.plot(target, label='target')
plt.legend();

R2 score

simplest possible model is to take the avg of all values and draw a straight line, then calculate the mean square error
the R2 score is 1 minus the error of our regression model divided by the error of the simplest possible model
if we have a good model, the error will be small compared to the simple model, thus R2 will be close to 1
for a bad model, the ratio of errors will be closer to 1, giving a small R2 values



In [50]:

    
from sklearn.metrics import r2_score
r2_score(target,predicted)









    Out[50]:





0.7406077428649428



In [ ]:

	0	1	2	4	5	6	7	8	9	10	11	12
0	0.00632	18.0	2.31	0.538	6.575	65.2	4.0900	1.0	296.0	15.3	396.90	4.98
1	0.02731	0.0	7.07	0.469	6.421	78.9	4.9671	2.0	242.0	17.8	396.90	9.14
2	0.02729	0.0	7.07	0.469	7.185	61.1	4.9671	2.0	242.0	17.8	392.83	4.03
3	0.03237	0.0	2.18	0.458	6.998	45.8	6.0622	3.0	222.0	18.7	394.63	2.94
4	0.06905	0.0	2.18	0.458	7.147	54.2	6.0622	3.0	222.0	18.7	396.90	5.33