notebook.community



In [10]:

    
# import
import graphlab as gl
import matplotlib.pyplot as plt



In [11]:

    
gl.canvas.set_target('ipynb')
%matplotlib inline



In [4]:

    
# reading the data
data = gl.SFrame.read_csv('data/Philadelphia_Crime_Rate_noNA.csv')
data.head(4)









    




Finished parsing file D:\Git\MachineLearning\ML_UoW\Course01_Regression\data\Philadelphia_Crime_Rate_noNA.csv






    




Parsing completed. Parsed 99 lines in 0.024024 secs.






    



------------------------------------------------------
Inferred types from first 100 line(s) of file as 
column_type_hints=[long,float,float,float,float,str,str]
If parsing fails due to incorrect types, you can correct
the inferred type list above and pass it to read_csv in
the column_type_hints argument
------------------------------------------------------






    




Finished parsing file D:\Git\MachineLearning\ML_UoW\Course01_Regression\data\Philadelphia_Crime_Rate_noNA.csv






    




Parsing completed. Parsed 99 lines in 0.020014 secs.






    Out[4]:





    
        HousePrice
        HsPrc ($10,000)
        CrimeRate
        MilesPhila
        PopChg
        Name
        County
    
    
        140463
        14.0463
        29.7
        10.0
        -1.0
        Abington
        Montgome
    
    
        113033
        11.3033
        24.1
        18.0
        4.0
        Ambler
        Montgome
    
    
        124186
        12.4186
        19.5
        25.0
        8.0
        Aston
        Delaware
    
    
        110490
        11.049
        49.4
        25.0
        2.7
        Bensalem
        Bucks
    

[4 rows x 7 columns]



In [8]:

    
# making a scatter plot
data.show(x='CrimeRate', y='HousePrice', view='Scatter Plot')

Fitting the Regression model



In [9]:

    
crime_model = gl.linear_regression.create(data,
                                         features=['CrimeRate'],
                                         target='HousePrice')









    




Linear regression:






    




--------------------------------------------------------






    




Number of examples          : 99






    




Number of features          : 1






    




Number of unpacked features : 1






    




Number of coefficients    : 2






    




Starting Newton Method






    




--------------------------------------------------------






    




+-----------+----------+--------------+--------------------+---------------+






    




| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |






    




+-----------+----------+--------------+--------------------+---------------+






    




| 1         | 2        | 1.062593     | 314982.574662      | 83468.940148  |






    




+-----------+----------+--------------+--------------------+---------------+






    




SUCCESS: Optimal solution found.



In [20]:

    
plt.plot(data['CrimeRate'], data['HousePrice'], '.',
        data['CrimeRate'], crime_model.predict(data), '-')









    Out[20]:





[<matplotlib.lines.Line2D at 0x20de12e8>,
 <matplotlib.lines.Line2D at 0x20de1390>]

Removing the outlier data



In [30]:

    
data2 = data[data['MilesPhila']!=0.0]



In [31]:

    
crime_model_noCC = gl.linear_regression.create(data2,
                                         features=['CrimeRate'],
                                         target='HousePrice')









    




Linear regression:






    




--------------------------------------------------------






    




Number of examples          : 98






    




Number of features          : 1






    




Number of unpacked features : 1






    




Number of coefficients    : 2






    




Starting Newton Method






    




--------------------------------------------------------






    




+-----------+----------+--------------+--------------------+---------------+






    




| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |






    




+-----------+----------+--------------+--------------------+---------------+






    




| 1         | 2        | 0.000501     | 315335.534886      | 78052.676125  |






    




+-----------+----------+--------------+--------------------+---------------+






    




SUCCESS: Optimal solution found.



In [32]:

    
plt.plot(data2['CrimeRate'], data2['HousePrice'], '.',
        data2['CrimeRate'], crime_model_noCC.predict(data2), '-')









    Out[32]:





[<matplotlib.lines.Line2D at 0x1d783b00>,
 <matplotlib.lines.Line2D at 0x1d783cc0>]

Comparing the co-efficieitns



In [33]:

    
print('data: ',crime_model.coefficients)
print('data2: ',crime_model_noCC.coefficients)









    



('data: ', Columns:
	name	str
	index	str
	value	float
	stderr	float

Rows: 2

Data:
+-------------+-------+----------------+---------------+
|     name    | index |     value      |     stderr    |
+-------------+-------+----------------+---------------+
| (intercept) |  None | 176626.046881  | 11245.5882194 |
|  CrimeRate  |  None | -576.804949058 |  226.90225951 |
+-------------+-------+----------------+---------------+
[2 rows x 4 columns]
)
('data2: ', Columns:
	name	str
	index	str
	value	float
	stderr	float

Rows: 2

Data:
+-------------+-------+----------------+---------------+
|     name    | index |     value      |     stderr    |
+-------------+-------+----------------+---------------+
| (intercept) |  None | 225204.604303  | 16404.0247514 |
|  CrimeRate  |  None | -2287.69717443 | 491.537478123 |
+-------------+-------+----------------+---------------+
[2 rows x 4 columns]
)



In [34]:

    
crime_model.get('coefficients')









    Out[34]:





    
        name
        index
        value
        stderr
    
    
        (intercept)
        None
        176626.046881
        11245.5882194
    
    
        CrimeRate
        None
        -576.804949058
        226.90225951
    

[2 rows x 4 columns]



In [35]:

    
crime_model_noCC.coefficients









    Out[35]:





    
        name
        index
        value
        stderr
    
    
        (intercept)
        None
        225204.604303
        16404.0247514
    
    
        CrimeRate
        None
        -2287.69717443
        491.537478123
    

[2 rows x 4 columns]

Removing the High End House



In [36]:

    
data_noHighPrice = data2[data2['HousePrice']<350000]



In [41]:

    
crime_model_noHighPrice = gl.linear_regression.create(data_noHighPrice,
                                         features=['CrimeRate'],
                                         target='HousePrice')









    




Linear regression:






    




--------------------------------------------------------






    




Number of examples          : 93






    




Number of features          : 1






    




Number of unpacked features : 1






    




Number of coefficients    : 2






    




Starting Newton Method






    




--------------------------------------------------------






    




+-----------+----------+--------------+--------------------+---------------+






    




| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |






    




+-----------+----------+--------------+--------------------+---------------+






    




| 1         | 2        | 0.000000     | 153105.996748      | 54958.023447  |






    




+-----------+----------+--------------+--------------------+---------------+






    




SUCCESS: Optimal solution found.



In [42]:

    
crime_model_noHighPrice.get('coefficients')









    Out[42]:





    
        name
        index
        value
        stderr
    
    
        (intercept)
        None
        199073.589615
        11932.5101105
    
    
        CrimeRate
        None
        -1837.71280989
        351.519609333
    

[2 rows x 4 columns]



In [43]:

    
crime_model_noCC.get('coefficients')









    Out[43]:





    
        name
        index
        value
        stderr
    
    
        (intercept)
        None
        225204.604303
        16404.0247514
    
    
        CrimeRate
        None
        -2287.69717443
        491.537478123
    

[2 rows x 4 columns]



In [ ]:

HousePrice	HsPrc ($10,000)	CrimeRate	MilesPhila	PopChg	Name	County
140463	14.0463	29.7	10.0	-1.0	Abington	Montgome
113033	11.3033	24.1	18.0	4.0	Ambler	Montgome
124186	12.4186	19.5	25.0	8.0	Aston	Delaware
110490	11.049	49.4	25.0	2.7	Bensalem	Bucks

name	index	value	stderr
(intercept)	None	176626.046881	11245.5882194
CrimeRate	None	-576.804949058	226.90225951

name	index	value	stderr
(intercept)	None	225204.604303	16404.0247514
CrimeRate	None	-2287.69717443	491.537478123

name	index	value	stderr
(intercept)	None	199073.589615	11932.5101105
CrimeRate	None	-1837.71280989	351.519609333