The Financial Journal (Global): Multiple Linear Regression of Raw Data, Standardized Data, and Normalized Data

Multiple Linear Regression of Raw Data, Standardized Data, and Normalized Data

**0_MacOS_Python_setup.txt**
# Install on Terminal of MacOS # 1. pandas #pip3 install -U pandas # 2. matplotlib #pip3 install -U matplotlib # 3. scikit-learn (sklearn) #pip3 install -U scikit-learn # 4. statsmodels #pip3 install -U statsmodels # 5. NumPy #pip3 install -U numpy

1_MacOS_Terminal.txt

########## Run Terminal on MacOS and execute
### TO UPDATE
cd "YOUR_WORKING_DIRECTORY"

####Multiple Linear Regression

#Raw Data X vs Raw Data Y
#python3 mlrrwstnm.py df.csv Y RM r

#Standardized Data X vs Raw Data Y
python3 mlrrwstnm.py df.csv Y RM s

#Normalized Data X vs Raw Data Y
#python3 mlrrwstnm.py df.csv Y RM n

Input Data files

df.csv

,CRIM,ZN,INDUS,CHAS,NOX,RM,AGE,DIS,RAD,TAX,PTRATIO,B,LSTAT,Y
0,0.00632,18.0,2.31,0.0,0.538,6.575,65.2,4.09,1.0,296.0,15.3,396.9,4.98,24.0
1,0.02731,0.0,7.07,0.0,0.469,6.421,78.9,4.9671,2.0,242.0,17.8,396.9,9.14,21.6
2,0.02729,0.0,7.07,0.0,0.469,7.185,61.1,4.9671,2.0,242.0,17.8,392.83,4.03,34.7
3,0.03237,0.0,2.18,0.0,0.458,6.998,45.8,6.0622,3.0,222.0,18.7,394.63,2.94,33.4
4,0.06905,0.0,2.18,0.0,0.458,7.147,54.2,6.0622,3.0,222.0,18.7,396.9,5.33,36.2
5,0.02985,0.0,2.18,0.0,0.458,6.43,58.7,6.0622,3.0,222.0,18.7,394.12,5.21,28.7
6,0.08829,12.5,7.87,0.0,0.524,6.012,66.6,5.5605,5.0,311.0,15.2,395.6,12.43,22.9
7,0.14455,12.5,7.87,0.0,0.524,6.172,96.1,5.9505,5.0,311.0,15.2,396.9,19.15,27.1
8,0.21124,12.5,7.87,0.0,0.524,5.631,100.0,6.0821,5.0,311.0,15.2,386.63,29.93,16.5
9,0.17004,12.5,7.87,0.0,0.524,6.004,85.9,6.5921,5.0,311.0,15.2,386.71,17.1,18.9
10,0.22489,12.5,7.87,0.0,0.524,6.377,94.3,6.3467,5.0,311.0,15.2,392.52,20.45,15.0
11,0.11747,12.5,7.87,0.0,0.524,6.009,82.9,6.2267,5.0,311.0,15.2,396.9,13.27,18.9
12,0.09378,12.5,7.87,0.0,0.524,5.889,39.0,5.4509,5.0,311.0,15.2,390.5,15.71,21.7
13,0.62976,0.0,8.14,0.0,0.538,5.949,61.8,4.7075,4.0,307.0,21.0,396.9,8.26,20.4
14,0.63796,0.0,8.14,0.0,0.538,6.096,84.5,4.4619,4.0,307.0,21.0,380.02,10.26,18.2
15,0.62739,0.0,8.14,0.0,0.538,5.834,56.5,4.4986,4.0,307.0,21.0,395.62,8.47,19.9
16,1.05393,0.0,8.14,0.0,0.538,5.935,29.3,4.4986,4.0,307.0,21.0,386.85,6.58,23.1
17,0.7842,0.0,8.14,0.0,0.538,5.99,81.7,4.2579,4.0,307.0,21.0,386.75,14.67,17.5
18,0.80271,0.0,8.14,0.0,0.538,5.456,36.6,3.7965,4.0,307.0,21.0,288.99,11.69,20.2
19,0.7258,0.0,8.14,0.0,0.538,5.727,69.5,3.7965,4.0,307.0,21.0,390.95,11.28,18.2
20,1.25179,0.0,8.14,0.0,0.538,5.57,98.1,3.7979,4.0,307.0,21.0,376.57,21.02,13.6
21,0.85204,0.0,8.14,0.0,0.538,5.965,89.2,4.0123,4.0,307.0,21.0,392.53,13.83,19.6
22,1.23247,0.0,8.14,0.0,0.538,6.142,91.7,3.9769,4.0,307.0,21.0,396.9,18.72,15.2
23,0.98843,0.0,8.14,0.0,0.538,5.813,100.0,4.0952,4.0,307.0,21.0,394.54,19.88,14.5
24,0.75026,0.0,8.14,0.0,0.538,5.924,94.1,4.3996,4.0,307.0,21.0,394.33,16.3,15.6
25,0.84054,0.0,8.14,0.0,0.538,5.599,85.7,4.4546,4.0,307.0,21.0,303.42,16.51,13.9
26,0.67191,0.0,8.14,0.0,0.538,5.813,90.3,4.682,4.0,307.0,21.0,376.88,14.81,16.6
27,0.95577,0.0,8.14,0.0,0.538,6.047,88.8,4.4534,4.0,307.0,21.0,306.38,17.28,14.8
28,0.77299,0.0,8.14,0.0,0.538,6.495,94.4,4.4547,4.0,307.0,21.0,387.94,12.8,18.4
29,1.00245,0.0,8.14,0.0,0.538,6.674,87.3,4.239,4.0,307.0,21.0,380.23,11.98,21.0
30,1.13081,0.0,8.14,0.0,0.538,5.713,94.1,4.233,4.0,307.0,21.0,360.17,22.6,12.7
31,1.35472,0.0,8.14,0.0,0.538,6.072,100.0,4.175,4.0,307.0,21.0,376.73,13.04,14.5
32,1.38799,0.0,8.14,0.0,0.538,5.95,82.0,3.99,4.0,307.0,21.0,232.6,27.71,13.2
33,1.15172,0.0,8.14,0.0,0.538,5.701,95.0,3.7872,4.0,307.0,21.0,358.77,18.35,13.1
34,1.61282,0.0,8.14,0.0,0.538,6.096,96.9,3.7598,4.0,307.0,21.0,248.31,20.34,13.5
35,0.06417,0.0,5.96,0.0,0.499,5.933,68.2,3.3603,5.0,279.0,19.2,396.9,9.68,18.9
36,0.09744,0.0,5.96,0.0,0.499,5.841,61.4,3.3779,5.0,279.0,19.2,377.56,11.41,20.0
37,0.08014,0.0,5.96,0.0,0.499,5.85,41.5,3.9342,5.0,279.0,19.2,396.9,8.77,21.0
38,0.17505,0.0,5.96,0.0,0.499,5.966,30.2,3.8473,5.0,279.0,19.2,393.43,10.13,24.7
39,0.02763,75.0,2.95,0.0,0.428,6.595,21.8,5.4011,3.0,252.0,18.3,395.63,4.32,30.8
40,0.03359,75.0,2.95,0.0,0.428,7.024,15.8,5.4011,3.0,252.0,18.3,395.62,1.98,34.9
41,0.12744,0.0,6.91,0.0,0.448,6.77,2.9,5.7209,3.0,233.0,17.9,385.41,4.84,26.6
42,0.1415,0.0,6.91,0.0,0.448,6.169,6.6,5.7209,3.0,233.0,17.9,383.37,5.81,25.3
43,0.15936,0.0,6.91,0.0,0.448,6.211,6.5,5.7209,3.0,233.0,17.9,394.46,7.44,24.7
44,0.12269,0.0,6.91,0.0,0.448,6.069,40.0,5.7209,3.0,233.0,17.9,389.39,9.55,21.2
45,0.17142,0.0,6.91,0.0,0.448,5.682,33.8,5.1004,3.0,233.0,17.9,396.9,10.21,19.3
46,0.18836,0.0,6.91,0.0,0.448,5.786,33.3,5.1004,3.0,233.0,17.9,396.9,14.15,20.0
47,0.22927,0.0,6.91,0.0,0.448,6.03,85.5,5.6894,3.0,233.0,17.9,392.74,18.8,16.6
48,0.25387,0.0,6.91,0.0,0.448,5.399,95.3,5.87,3.0,233.0,17.9,396.9,30.81,14.4
49,0.21977,0.0,6.91,0.0,0.448,5.602,62.0,6.0877,3.0,233.0,17.9,396.9,16.2,19.4
50,0.08873,21.0,5.64,0.0,0.439,5.963,45.7,6.8147,4.0,243.0,16.8,395.56,13.45,19.7
51,0.04337,21.0,5.64,0.0,0.439,6.115,63.0,6.8147,4.0,243.0,16.8,393.97,9.43,20.5
52,0.0536,21.0,5.64,0.0,0.439,6.511,21.1,6.8147,4.0,243.0,16.8,396.9,5.28,25.0
53,0.04981,21.0,5.64,0.0,0.439,5.998,21.4,6.8147,4.0,243.0,16.8,396.9,8.43,23.4
54,0.0136,75.0,4.0,0.0,0.41,5.888,47.6,7.3197,3.0,469.0,21.1,396.9,14.8,18.9
55,0.01311,90.0,1.22,0.0,0.403,7.249,21.9,8.6966,5.0,226.0,17.9,395.93,4.81,35.4
56,0.02055,85.0,0.74,0.0,0.41,6.383,35.7,9.1876,2.0,313.0,17.3,396.9,5.77,24.7
57,0.01432,100.0,1.32,0.0,0.411,6.816,40.5,8.3248,5.0,256.0,15.1,392.9,3.95,31.6
58,0.15445,25.0,5.13,0.0,0.453,6.145,29.2,7.8148,8.0,284.0,19.7,390.68,6.86,23.3
59,0.10328,25.0,5.13,0.0,0.453,5.927,47.2,6.932,8.0,284.0,19.7,396.9,9.22,19.6
60,0.14932,25.0,5.13,0.0,0.453,5.741,66.2,7.2254,8.0,284.0,19.7,395.11,13.15,18.7
61,0.17171,25.0,5.13,0.0,0.453,5.966,93.4,6.8185,8.0,284.0,19.7,378.08,14.44,16.0
62,0.11027,25.0,5.13,0.0,0.453,6.456,67.8,7.2255,8.0,284.0,19.7,396.9,6.73,22.2
63,0.1265,25.0,5.13,0.0,0.453,6.762,43.4,7.9809,8.0,284.0,19.7,395.58,9.5,25.0
64,0.01951,17.5,1.38,0.0,0.4161,7.104,59.5,9.2229,3.0,216.0,18.6,393.24,8.05,33.0
65,0.03584,80.0,3.37,0.0,0.398,6.29,17.8,6.6115,4.0,337.0,16.1,396.9,4.67,23.5
66,0.04379,80.0,3.37,0.0,0.398,5.787,31.1,6.6115,4.0,337.0,16.1,396.9,10.24,19.4
67,0.05789,12.5,6.07,0.0,0.409,5.878,21.4,6.498,4.0,345.0,18.9,396.21,8.1,22.0
68,0.13554,12.5,6.07,0.0,0.409,5.594,36.8,6.498,4.0,345.0,18.9,396.9,13.09,17.4
69,0.12816,12.5,6.07,0.0,0.409,5.885,33.0,6.498,4.0,345.0,18.9,396.9,8.79,20.9
70,0.08826,0.0,10.81,0.0,0.413,6.417,6.6,5.2873,4.0,305.0,19.2,383.73,6.72,24.2
71,0.15876,0.0,10.81,0.0,0.413,5.961,17.5,5.2873,4.0,305.0,19.2,376.94,9.88,21.7
72,0.09164,0.0,10.81,0.0,0.413,6.065,7.8,5.2873,4.0,305.0,19.2,390.91,5.52,22.8
73,0.19539,0.0,10.81,0.0,0.413,6.245,6.2,5.2873,4.0,305.0,19.2,377.17,7.54,23.4
74,0.07896,0.0,12.83,0.0,0.437,6.273,6.0,4.2515,5.0,398.0,18.7,394.92,6.78,24.1
75,0.09512,0.0,12.83,0.0,0.437,6.286,45.0,4.5026,5.0,398.0,18.7,383.23,8.94,21.4
76,0.10153,0.0,12.83,0.0,0.437,6.279,74.5,4.0522,5.0,398.0,18.7,373.66,11.97,20.0
77,0.08707,0.0,12.83,0.0,0.437,6.14,45.8,4.0905,5.0,398.0,18.7,386.96,10.27,20.8
78,0.05646,0.0,12.83,0.0,0.437,6.232,53.7,5.0141,5.0,398.0,18.7,386.4,12.34,21.2
79,0.08387,0.0,12.83,0.0,0.437,5.874,36.6,4.5026,5.0,398.0,18.7,396.06,9.1,20.3
80,0.04113,25.0,4.86,0.0,0.426,6.727,33.5,5.4007,4.0,281.0,19.0,396.9,5.29,28.0
81,0.04462,25.0,4.86,0.0,0.426,6.619,70.4,5.4007,4.0,281.0,19.0,395.63,7.22,23.9
82,0.03659,25.0,4.86,0.0,0.426,6.302,32.2,5.4007,4.0,281.0,19.0,396.9,6.72,24.8
83,0.03551,25.0,4.86,0.0,0.426,6.167,46.7,5.4007,4.0,281.0,19.0,390.64,7.51,22.9
84,0.05059,0.0,4.49,0.0,0.449,6.389,48.0,4.7794,3.0,247.0,18.5,396.9,9.62,23.9
85,0.05735,0.0,4.49,0.0,0.449,6.63,56.1,4.4377,3.0,247.0,18.5,392.3,6.53,26.6
86,0.05188,0.0,4.49,0.0,0.449,6.015,45.1,4.4272,3.0,247.0,18.5,395.99,12.86,22.5
87,0.07151,0.0,4.49,0.0,0.449,6.121,56.8,3.7476,3.0,247.0,18.5,395.15,8.44,22.2
88,0.0566,0.0,3.41,0.0,0.489,7.007,86.3,3.4217,2.0,270.0,17.8,396.9,5.5,23.6
89,0.05302,0.0,3.41,0.0,0.489,7.079,63.1,3.4145,2.0,270.0,17.8,396.06,5.7,28.7
90,0.04684,0.0,3.41,0.0,0.489,6.417,66.1,3.0923,2.0,270.0,17.8,392.18,8.81,22.6
91,0.03932,0.0,3.41,0.0,0.489,6.405,73.9,3.0921,2.0,270.0,17.8,393.55,8.2,22.0
92,0.04203,28.0,15.04,0.0,0.464,6.442,53.6,3.6659,4.0,270.0,18.2,395.01,8.16,22.9
93,0.02875,28.0,15.04,0.0,0.464,6.211,28.9,3.6659,4.0,270.0,18.2,396.33,6.21,25.0
94,0.04294,28.0,15.04,0.0,0.464,6.249,77.3,3.615,4.0,270.0,18.2,396.9,10.59,20.6
95,0.12204,0.0,2.89,0.0,0.445,6.625,57.8,3.4952,2.0,276.0,18.0,357.98,6.65,28.4
96,0.11504,0.0,2.89,0.0,0.445,6.163,69.6,3.4952,2.0,276.0,18.0,391.83,11.34,21.4
97,0.12083,0.0,2.89,0.0,0.445,8.069,76.0,3.4952,2.0,276.0,18.0,396.9,4.21,38.7
98,0.08187,0.0,2.89,0.0,0.445,7.82,36.9,3.4952,2.0,276.0,18.0,393.53,3.57,43.8
99,0.0686,0.0,2.89,0.0,0.445,7.416,62.5,3.4952,2.0,276.0,18.0,396.9,6.19,33.2
100,0.14866,0.0,8.56,0.0,0.52,6.727,79.9,2.7778,5.0,384.0,20.9,394.76,9.42,27.5
101,0.11432,0.0,8.56,0.0,0.52,6.781,71.3,2.8561,5.0,384.0,20.9,395.58,7.67,26.5
102,0.22876,0.0,8.56,0.0,0.52,6.405,85.4,2.7147,5.0,384.0,20.9,70.8,10.63,18.6
103,0.21161,0.0,8.56,0.0,0.52,6.137,87.4,2.7147,5.0,384.0,20.9,394.47,13.44,19.3
104,0.1396,0.0,8.56,0.0,0.52,6.167,90.0,2.421,5.0,384.0,20.9,392.69,12.33,20.1
105,0.13262,0.0,8.56,0.0,0.52,5.851,96.7,2.1069,5.0,384.0,20.9,394.05,16.47,19.5
106,0.1712,0.0,8.56,0.0,0.52,5.836,91.9,2.211,5.0,384.0,20.9,395.67,18.66,19.5
107,0.13117,0.0,8.56,0.0,0.52,6.127,85.2,2.1224,5.0,384.0,20.9,387.69,14.09,20.4
108,0.12802,0.0,8.56,0.0,0.52,6.474,97.1,2.4329,5.0,384.0,20.9,395.24,12.27,19.8
109,0.26363,0.0,8.56,0.0,0.52,6.229,91.2,2.5451,5.0,384.0,20.9,391.23,15.55,19.4
110,0.10793,0.0,8.56,0.0,0.52,6.195,54.4,2.7778,5.0,384.0,20.9,393.49,13.0,21.7
111,0.10084,0.0,10.01,0.0,0.547,6.715,81.6,2.6775,6.0,432.0,17.8,395.59,10.16,22.8
112,0.12329,0.0,10.01,0.0,0.547,5.913,92.9,2.3534,6.0,432.0,17.8,394.95,16.21,18.8
113,0.22212,0.0,10.01,0.0,0.547,6.092,95.4,2.548,6.0,432.0,17.8,396.9,17.09,18.7
114,0.14231,0.0,10.01,0.0,0.547,6.254,84.2,2.2565,6.0,432.0,17.8,388.74,10.45,18.5
115,0.17134,0.0,10.01,0.0,0.547,5.928,88.2,2.4631,6.0,432.0,17.8,344.91,15.76,18.3
116,0.13158,0.0,10.01,0.0,0.547,6.176,72.5,2.7301,6.0,432.0,17.8,393.3,12.04,21.2
117,0.15098,0.0,10.01,0.0,0.547,6.021,82.6,2.7474,6.0,432.0,17.8,394.51,10.3,19.2
118,0.13058,0.0,10.01,0.0,0.547,5.872,73.1,2.4775,6.0,432.0,17.8,338.63,15.37,20.4
119,0.14476,0.0,10.01,0.0,0.547,5.731,65.2,2.7592,6.0,432.0,17.8,391.5,13.61,19.3
120,0.06899,0.0,25.65,0.0,0.581,5.87,69.7,2.2577,2.0,188.0,19.1,389.15,14.37,22.0
121,0.07165,0.0,25.65,0.0,0.581,6.004,84.1,2.1974,2.0,188.0,19.1,377.67,14.27,20.3
122,0.09299,0.0,25.65,0.0,0.581,5.961,92.9,2.0869,2.0,188.0,19.1,378.09,17.93,20.5
123,0.15038,0.0,25.65,0.0,0.581,5.856,97.0,1.9444,2.0,188.0,19.1,370.31,25.41,17.3
124,0.09849,0.0,25.65,0.0,0.581,5.879,95.8,2.0063,2.0,188.0,19.1,379.38,17.58,18.8
125,0.16902,0.0,25.65,0.0,0.581,5.986,88.4,1.9929,2.0,188.0,19.1,385.02,14.81,21.4
126,0.38735,0.0,25.65,0.0,0.581,5.613,95.6,1.7572,2.0,188.0,19.1,359.29,27.26,15.7
127,0.25915,0.0,21.89,0.0,0.624,5.693,96.0,1.7883,4.0,437.0,21.2,392.11,17.19,16.2
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261,0.53412,20.0,3.97,0.0,0.647,7.52,89.4,2.1398,5.0,264.0,13.0,388.37,7.26,43.1
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288,0.0459,52.5,5.32,0.0,0.405,6.315,45.6,7.3172,6.0,293.0,16.6,396.9,7.6,22.3
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321,0.18159,0.0,7.38,0.0,0.493,6.376,54.3,4.5404,5.0,287.0,19.6,396.9,6.87,23.1
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323,0.28392,0.0,7.38,0.0,0.493,5.708,74.3,4.7211,5.0,287.0,19.6,391.13,11.74,18.5
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344,0.03049,55.0,3.78,0.0,0.484,6.874,28.1,6.4654,5.0,370.0,17.6,387.97,4.61,31.2
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346,0.06162,0.0,4.39,0.0,0.442,5.898,52.3,8.0136,3.0,352.0,18.8,364.61,12.67,17.2
347,0.0187,85.0,4.15,0.0,0.429,6.516,27.7,8.5353,4.0,351.0,17.9,392.43,6.36,23.1
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352,0.07244,60.0,1.69,0.0,0.411,5.884,18.5,10.7103,4.0,411.0,18.3,392.33,7.79,18.6
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358,5.20177,0.0,18.1,1.0,0.77,6.127,83.4,2.7227,24.0,666.0,20.2,395.43,11.48,22.7
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362,3.67822,0.0,18.1,0.0,0.77,5.362,96.2,2.1036,24.0,666.0,20.2,380.79,10.19,20.8
363,4.22239,0.0,18.1,1.0,0.77,5.803,89.0,1.9047,24.0,666.0,20.2,353.04,14.64,16.8
364,3.47428,0.0,18.1,1.0,0.718,8.78,82.9,1.9047,24.0,666.0,20.2,354.55,5.29,21.9
365,4.55587,0.0,18.1,0.0,0.718,3.561,87.9,1.6132,24.0,666.0,20.2,354.7,7.12,27.5
366,3.69695,0.0,18.1,0.0,0.718,4.963,91.4,1.7523,24.0,666.0,20.2,316.03,14.0,21.9
367,13.5222,0.0,18.1,0.0,0.631,3.863,100.0,1.5106,24.0,666.0,20.2,131.42,13.33,23.1
368,4.89822,0.0,18.1,0.0,0.631,4.97,100.0,1.3325,24.0,666.0,20.2,375.52,3.26,50.0
369,5.66998,0.0,18.1,1.0,0.631,6.683,96.8,1.3567,24.0,666.0,20.2,375.33,3.73,50.0
370,6.53876,0.0,18.1,1.0,0.631,7.016,97.5,1.2024,24.0,666.0,20.2,392.05,2.96,50.0
371,9.2323,0.0,18.1,0.0,0.631,6.216,100.0,1.1691,24.0,666.0,20.2,366.15,9.53,50.0
372,8.26725,0.0,18.1,1.0,0.668,5.875,89.6,1.1296,24.0,666.0,20.2,347.88,8.88,50.0
373,11.1081,0.0,18.1,0.0,0.668,4.906,100.0,1.1742,24.0,666.0,20.2,396.9,34.77,13.8
374,18.4982,0.0,18.1,0.0,0.668,4.138,100.0,1.137,24.0,666.0,20.2,396.9,37.97,13.8
375,19.6091,0.0,18.1,0.0,0.671,7.313,97.9,1.3163,24.0,666.0,20.2,396.9,13.44,15.0
376,15.288,0.0,18.1,0.0,0.671,6.649,93.3,1.3449,24.0,666.0,20.2,363.02,23.24,13.9
377,9.82349,0.0,18.1,0.0,0.671,6.794,98.8,1.358,24.0,666.0,20.2,396.9,21.24,13.3
378,23.6482,0.0,18.1,0.0,0.671,6.38,96.2,1.3861,24.0,666.0,20.2,396.9,23.69,13.1
379,17.8667,0.0,18.1,0.0,0.671,6.223,100.0,1.3861,24.0,666.0,20.2,393.74,21.78,10.2
380,88.9762,0.0,18.1,0.0,0.671,6.968,91.9,1.4165,24.0,666.0,20.2,396.9,17.21,10.4
381,15.8744,0.0,18.1,0.0,0.671,6.545,99.1,1.5192,24.0,666.0,20.2,396.9,21.08,10.9
382,9.18702,0.0,18.1,0.0,0.7,5.536,100.0,1.5804,24.0,666.0,20.2,396.9,23.6,11.3
383,7.99248,0.0,18.1,0.0,0.7,5.52,100.0,1.5331,24.0,666.0,20.2,396.9,24.56,12.3
384,20.0849,0.0,18.1,0.0,0.7,4.368,91.2,1.4395,24.0,666.0,20.2,285.83,30.63,8.8
385,16.8118,0.0,18.1,0.0,0.7,5.277,98.1,1.4261,24.0,666.0,20.2,396.9,30.81,7.2
386,24.3938,0.0,18.1,0.0,0.7,4.652,100.0,1.4672,24.0,666.0,20.2,396.9,28.28,10.5
387,22.5971,0.0,18.1,0.0,0.7,5.0,89.5,1.5184,24.0,666.0,20.2,396.9,31.99,7.4
388,14.3337,0.0,18.1,0.0,0.7,4.88,100.0,1.5895,24.0,666.0,20.2,372.92,30.62,10.2
389,8.15174,0.0,18.1,0.0,0.7,5.39,98.9,1.7281,24.0,666.0,20.2,396.9,20.85,11.5
390,6.96215,0.0,18.1,0.0,0.7,5.713,97.0,1.9265,24.0,666.0,20.2,394.43,17.11,15.1
391,5.29305,0.0,18.1,0.0,0.7,6.051,82.5,2.1678,24.0,666.0,20.2,378.38,18.76,23.2
392,11.5779,0.0,18.1,0.0,0.7,5.036,97.0,1.77,24.0,666.0,20.2,396.9,25.68,9.7
393,8.64476,0.0,18.1,0.0,0.693,6.193,92.6,1.7912,24.0,666.0,20.2,396.9,15.17,13.8
394,13.3598,0.0,18.1,0.0,0.693,5.887,94.7,1.7821,24.0,666.0,20.2,396.9,16.35,12.7
395,8.71675,0.0,18.1,0.0,0.693,6.471,98.8,1.7257,24.0,666.0,20.2,391.98,17.12,13.1
396,5.87205,0.0,18.1,0.0,0.693,6.405,96.0,1.6768,24.0,666.0,20.2,396.9,19.37,12.5
397,7.67202,0.0,18.1,0.0,0.693,5.747,98.9,1.6334,24.0,666.0,20.2,393.1,19.92,8.5
398,38.3518,0.0,18.1,0.0,0.693,5.453,100.0,1.4896,24.0,666.0,20.2,396.9,30.59,5.0
399,9.91655,0.0,18.1,0.0,0.693,5.852,77.8,1.5004,24.0,666.0,20.2,338.16,29.97,6.3
400,25.0461,0.0,18.1,0.0,0.693,5.987,100.0,1.5888,24.0,666.0,20.2,396.9,26.77,5.6
401,14.2362,0.0,18.1,0.0,0.693,6.343,100.0,1.5741,24.0,666.0,20.2,396.9,20.32,7.2
402,9.59571,0.0,18.1,0.0,0.693,6.404,100.0,1.639,24.0,666.0,20.2,376.11,20.31,12.1
403,24.8017,0.0,18.1,0.0,0.693,5.349,96.0,1.7028,24.0,666.0,20.2,396.9,19.77,8.3
404,41.5292,0.0,18.1,0.0,0.693,5.531,85.4,1.6074,24.0,666.0,20.2,329.46,27.38,8.5
405,67.9208,0.0,18.1,0.0,0.693,5.683,100.0,1.4254,24.0,666.0,20.2,384.97,22.98,5.0
406,20.7162,0.0,18.1,0.0,0.659,4.138,100.0,1.1781,24.0,666.0,20.2,370.22,23.34,11.9
407,11.9511,0.0,18.1,0.0,0.659,5.608,100.0,1.2852,24.0,666.0,20.2,332.09,12.13,27.9
408,7.40389,0.0,18.1,0.0,0.597,5.617,97.9,1.4547,24.0,666.0,20.2,314.64,26.4,17.2
409,14.4383,0.0,18.1,0.0,0.597,6.852,100.0,1.4655,24.0,666.0,20.2,179.36,19.78,27.5
410,51.1358,0.0,18.1,0.0,0.597,5.757,100.0,1.413,24.0,666.0,20.2,2.6,10.11,15.0
411,14.0507,0.0,18.1,0.0,0.597,6.657,100.0,1.5275,24.0,666.0,20.2,35.05,21.22,17.2
412,18.811,0.0,18.1,0.0,0.597,4.628,100.0,1.5539,24.0,666.0,20.2,28.79,34.37,17.9
413,28.6558,0.0,18.1,0.0,0.597,5.155,100.0,1.5894,24.0,666.0,20.2,210.97,20.08,16.3
414,45.7461,0.0,18.1,0.0,0.693,4.519,100.0,1.6582,24.0,666.0,20.2,88.27,36.98,7.0
415,18.0846,0.0,18.1,0.0,0.679,6.434,100.0,1.8347,24.0,666.0,20.2,27.25,29.05,7.2
416,10.8342,0.0,18.1,0.0,0.679,6.782,90.8,1.8195,24.0,666.0,20.2,21.57,25.79,7.5
417,25.9406,0.0,18.1,0.0,0.679,5.304,89.1,1.6475,24.0,666.0,20.2,127.36,26.64,10.4
418,73.5341,0.0,18.1,0.0,0.679,5.957,100.0,1.8026,24.0,666.0,20.2,16.45,20.62,8.8
419,11.8123,0.0,18.1,0.0,0.718,6.824,76.5,1.794,24.0,666.0,20.2,48.45,22.74,8.4
420,11.0874,0.0,18.1,0.0,0.718,6.411,100.0,1.8589,24.0,666.0,20.2,318.75,15.02,16.7
421,7.02259,0.0,18.1,0.0,0.718,6.006,95.3,1.8746,24.0,666.0,20.2,319.98,15.7,14.2
422,12.0482,0.0,18.1,0.0,0.614,5.648,87.6,1.9512,24.0,666.0,20.2,291.55,14.1,20.8
423,7.05042,0.0,18.1,0.0,0.614,6.103,85.1,2.0218,24.0,666.0,20.2,2.52,23.29,13.4
424,8.79212,0.0,18.1,0.0,0.584,5.565,70.6,2.0635,24.0,666.0,20.2,3.65,17.16,11.7
425,15.8603,0.0,18.1,0.0,0.679,5.896,95.4,1.9096,24.0,666.0,20.2,7.68,24.39,8.3
426,12.2472,0.0,18.1,0.0,0.584,5.837,59.7,1.9976,24.0,666.0,20.2,24.65,15.69,10.2
427,37.6619,0.0,18.1,0.0,0.679,6.202,78.7,1.8629,24.0,666.0,20.2,18.82,14.52,10.9
428,7.36711,0.0,18.1,0.0,0.679,6.193,78.1,1.9356,24.0,666.0,20.2,96.73,21.52,11.0
429,9.33889,0.0,18.1,0.0,0.679,6.38,95.6,1.9682,24.0,666.0,20.2,60.72,24.08,9.5
430,8.49213,0.0,18.1,0.0,0.584,6.348,86.1,2.0527,24.0,666.0,20.2,83.45,17.64,14.5
431,10.0623,0.0,18.1,0.0,0.584,6.833,94.3,2.0882,24.0,666.0,20.2,81.33,19.69,14.1
432,6.44405,0.0,18.1,0.0,0.584,6.425,74.8,2.2004,24.0,666.0,20.2,97.95,12.03,16.1
433,5.58107,0.0,18.1,0.0,0.713,6.436,87.9,2.3158,24.0,666.0,20.2,100.19,16.22,14.3
434,13.9134,0.0,18.1,0.0,0.713,6.208,95.0,2.2222,24.0,666.0,20.2,100.63,15.17,11.7
435,11.1604,0.0,18.1,0.0,0.74,6.629,94.6,2.1247,24.0,666.0,20.2,109.85,23.27,13.4
436,14.4208,0.0,18.1,0.0,0.74,6.461,93.3,2.0026,24.0,666.0,20.2,27.49,18.05,9.6
437,15.1772,0.0,18.1,0.0,0.74,6.152,100.0,1.9142,24.0,666.0,20.2,9.32,26.45,8.7
438,13.6781,0.0,18.1,0.0,0.74,5.935,87.9,1.8206,24.0,666.0,20.2,68.95,34.02,8.4
439,9.39063,0.0,18.1,0.0,0.74,5.627,93.9,1.8172,24.0,666.0,20.2,396.9,22.88,12.8
440,22.0511,0.0,18.1,0.0,0.74,5.818,92.4,1.8662,24.0,666.0,20.2,391.45,22.11,10.5
441,9.72418,0.0,18.1,0.0,0.74,6.406,97.2,2.0651,24.0,666.0,20.2,385.96,19.52,17.1
442,5.66637,0.0,18.1,0.0,0.74,6.219,100.0,2.0048,24.0,666.0,20.2,395.69,16.59,18.4
443,9.96654,0.0,18.1,0.0,0.74,6.485,100.0,1.9784,24.0,666.0,20.2,386.73,18.85,15.4
444,12.8023,0.0,18.1,0.0,0.74,5.854,96.6,1.8956,24.0,666.0,20.2,240.52,23.79,10.8
445,10.6718,0.0,18.1,0.0,0.74,6.459,94.8,1.9879,24.0,666.0,20.2,43.06,23.98,11.8
446,6.28807,0.0,18.1,0.0,0.74,6.341,96.4,2.072,24.0,666.0,20.2,318.01,17.79,14.9
447,9.92485,0.0,18.1,0.0,0.74,6.251,96.6,2.198,24.0,666.0,20.2,388.52,16.44,12.6
448,9.32909,0.0,18.1,0.0,0.713,6.185,98.7,2.2616,24.0,666.0,20.2,396.9,18.13,14.1
449,7.52601,0.0,18.1,0.0,0.713,6.417,98.3,2.185,24.0,666.0,20.2,304.21,19.31,13.0
450,6.71772,0.0,18.1,0.0,0.713,6.749,92.6,2.3236,24.0,666.0,20.2,0.32,17.44,13.4
451,5.44114,0.0,18.1,0.0,0.713,6.655,98.2,2.3552,24.0,666.0,20.2,355.29,17.73,15.2
452,5.09017,0.0,18.1,0.0,0.713,6.297,91.8,2.3682,24.0,666.0,20.2,385.09,17.27,16.1
453,8.24809,0.0,18.1,0.0,0.713,7.393,99.3,2.4527,24.0,666.0,20.2,375.87,16.74,17.8
454,9.51363,0.0,18.1,0.0,0.713,6.728,94.1,2.4961,24.0,666.0,20.2,6.68,18.71,14.9
455,4.75237,0.0,18.1,0.0,0.713,6.525,86.5,2.4358,24.0,666.0,20.2,50.92,18.13,14.1
456,4.66883,0.0,18.1,0.0,0.713,5.976,87.9,2.5806,24.0,666.0,20.2,10.48,19.01,12.7
457,8.20058,0.0,18.1,0.0,0.713,5.936,80.3,2.7792,24.0,666.0,20.2,3.5,16.94,13.5
458,7.75223,0.0,18.1,0.0,0.713,6.301,83.7,2.7831,24.0,666.0,20.2,272.21,16.23,14.9
459,6.80117,0.0,18.1,0.0,0.713,6.081,84.4,2.7175,24.0,666.0,20.2,396.9,14.7,20.0
460,4.81213,0.0,18.1,0.0,0.713,6.701,90.0,2.5975,24.0,666.0,20.2,255.23,16.42,16.4
461,3.69311,0.0,18.1,0.0,0.713,6.376,88.4,2.5671,24.0,666.0,20.2,391.43,14.65,17.7
462,6.65492,0.0,18.1,0.0,0.713,6.317,83.0,2.7344,24.0,666.0,20.2,396.9,13.99,19.5
463,5.82115,0.0,18.1,0.0,0.713,6.513,89.9,2.8016,24.0,666.0,20.2,393.82,10.29,20.2
464,7.83932,0.0,18.1,0.0,0.655,6.209,65.4,2.9634,24.0,666.0,20.2,396.9,13.22,21.4
465,3.1636,0.0,18.1,0.0,0.655,5.759,48.2,3.0665,24.0,666.0,20.2,334.4,14.13,19.9
466,3.77498,0.0,18.1,0.0,0.655,5.952,84.7,2.8715,24.0,666.0,20.2,22.01,17.15,19.0
467,4.42228,0.0,18.1,0.0,0.584,6.003,94.5,2.5403,24.0,666.0,20.2,331.29,21.32,19.1
468,15.5757,0.0,18.1,0.0,0.58,5.926,71.0,2.9084,24.0,666.0,20.2,368.74,18.13,19.1
469,13.0751,0.0,18.1,0.0,0.58,5.713,56.7,2.8237,24.0,666.0,20.2,396.9,14.76,20.1
470,4.34879,0.0,18.1,0.0,0.58,6.167,84.0,3.0334,24.0,666.0,20.2,396.9,16.29,19.9
471,4.03841,0.0,18.1,0.0,0.532,6.229,90.7,3.0993,24.0,666.0,20.2,395.33,12.87,19.6
472,3.56868,0.0,18.1,0.0,0.58,6.437,75.0,2.8965,24.0,666.0,20.2,393.37,14.36,23.2
473,4.64689,0.0,18.1,0.0,0.614,6.98,67.6,2.5329,24.0,666.0,20.2,374.68,11.66,29.8
474,8.05579,0.0,18.1,0.0,0.584,5.427,95.4,2.4298,24.0,666.0,20.2,352.58,18.14,13.8
475,6.39312,0.0,18.1,0.0,0.584,6.162,97.4,2.206,24.0,666.0,20.2,302.76,24.1,13.3
476,4.87141,0.0,18.1,0.0,0.614,6.484,93.6,2.3053,24.0,666.0,20.2,396.21,18.68,16.7
477,15.0234,0.0,18.1,0.0,0.614,5.304,97.3,2.1007,24.0,666.0,20.2,349.48,24.91,12.0
478,10.233,0.0,18.1,0.0,0.614,6.185,96.7,2.1705,24.0,666.0,20.2,379.7,18.03,14.6
479,14.3337,0.0,18.1,0.0,0.614,6.229,88.0,1.9512,24.0,666.0,20.2,383.32,13.11,21.4
480,5.82401,0.0,18.1,0.0,0.532,6.242,64.7,3.4242,24.0,666.0,20.2,396.9,10.74,23.0
481,5.70818,0.0,18.1,0.0,0.532,6.75,74.9,3.3317,24.0,666.0,20.2,393.07,7.74,23.7
482,5.73116,0.0,18.1,0.0,0.532,7.061,77.0,3.4106,24.0,666.0,20.2,395.28,7.01,25.0
483,2.81838,0.0,18.1,0.0,0.532,5.762,40.3,4.0983,24.0,666.0,20.2,392.92,10.42,21.8
484,2.37857,0.0,18.1,0.0,0.583,5.871,41.9,3.724,24.0,666.0,20.2,370.73,13.34,20.6
485,3.67367,0.0,18.1,0.0,0.583,6.312,51.9,3.9917,24.0,666.0,20.2,388.62,10.58,21.2
486,5.69175,0.0,18.1,0.0,0.583,6.114,79.8,3.5459,24.0,666.0,20.2,392.68,14.98,19.1
487,4.83567,0.0,18.1,0.0,0.583,5.905,53.2,3.1523,24.0,666.0,20.2,388.22,11.45,20.6
488,0.15086,0.0,27.74,0.0,0.609,5.454,92.7,1.8209,4.0,711.0,20.1,395.09,18.06,15.2
489,0.18337,0.0,27.74,0.0,0.609,5.414,98.3,1.7554,4.0,711.0,20.1,344.05,23.97,7.0
490,0.20746,0.0,27.74,0.0,0.609,5.093,98.0,1.8226,4.0,711.0,20.1,318.43,29.68,8.1
491,0.10574,0.0,27.74,0.0,0.609,5.983,98.8,1.8681,4.0,711.0,20.1,390.11,18.07,13.6
492,0.11132,0.0,27.74,0.0,0.609,5.983,83.5,2.1099,4.0,711.0,20.1,396.9,13.35,20.1
493,0.17331,0.0,9.69,0.0,0.585,5.707,54.0,2.3817,6.0,391.0,19.2,396.9,12.01,21.8
494,0.27957,0.0,9.69,0.0,0.585,5.926,42.6,2.3817,6.0,391.0,19.2,396.9,13.59,24.5
495,0.17899,0.0,9.69,0.0,0.585,5.67,28.8,2.7986,6.0,391.0,19.2,393.29,17.6,23.1
496,0.2896,0.0,9.69,0.0,0.585,5.39,72.9,2.7986,6.0,391.0,19.2,396.9,21.14,19.7
497,0.26838,0.0,9.69,0.0,0.585,5.794,70.6,2.8927,6.0,391.0,19.2,396.9,14.1,18.3
498,0.23912,0.0,9.69,0.0,0.585,6.019,65.3,2.4091,6.0,391.0,19.2,396.9,12.92,21.2
499,0.17783,0.0,9.69,0.0,0.585,5.569,73.5,2.3999,6.0,391.0,19.2,395.77,15.1,17.5
500,0.22438,0.0,9.69,0.0,0.585,6.027,79.7,2.4982,6.0,391.0,19.2,396.9,14.33,16.8
501,0.06263,0.0,11.93,0.0,0.573,6.593,69.1,2.4786,1.0,273.0,21.0,391.99,9.67,22.4
502,0.04527,0.0,11.93,0.0,0.573,6.12,76.7,2.2875,1.0,273.0,21.0,396.9,9.08,20.6
503,0.06076,0.0,11.93,0.0,0.573,6.976,91.0,2.1675,1.0,273.0,21.0,396.9,5.64,23.9
504,0.10959,0.0,11.93,0.0,0.573,6.794,89.3,2.3889,1.0,273.0,21.0,393.45,6.48,22.0
505,0.04741,0.0,11.93,0.0,0.573,6.03,80.8,2.505,1.0,273.0,21.0,396.9,7.88,11.9

Python files

mlrrwstnm.py

############### Multiple Linear Regression of Raw Data, Standardized Data, and Normalized Data#####

########## Run this script on Terminal of MacOS as follows:
#
#python3 mlrrwstnm.py (csv data file) (dependent variable Y) (specified single independent variable x) (x conversion)
#
#For instance,
#python3 mlrrwstnm.py df.csv Y RM s

########## import

import sys
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
from sklearn import linear_model
from sklearn.preprocessing import StandardScaler
from sklearn.preprocessing import MinMaxScaler
import statsmodels.api as sm

########## arguments

dfname = str(sys.argv[1]) # e.g., df.csv
yname = str(sys.argv[2]) # e.g., Y (dependent vairible)
xname = str(sys.argv[3]) # e.g., RM (one of multiple indepdent variables to show)
xconv = str(sys.argv[4]) # e.g., r (raw X data), s (standardized X data), or n (normalized X data)

########### load csv dataset

##dt = datasets.load_boston()
##
## Boston house price dataset dict-keys
##
##print(type(dt))
##<class 'sklearn.utils.Bunch'>
##
##print(dt.keys())
##dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename'])
##
##print(pd.DataFrame(dt.data, columns=boston.feature_names))
'''
CRIM ZN INDUS CHAS NOX ... RAD TAX PTRATIO B LSTAT
0 0.00632 18.0 2.31 0.0 0.538 ... 1.0 296.0 15.3 396.90 4.98
1 0.02731 0.0 7.07 0.0 0.469 ... 2.0 242.0 17.8 396.90 9.14
2 0.02729 0.0 7.07 0.0 0.469 ... 2.0 242.0 17.8 392.83 4.03
3 0.03237 0.0 2.18 0.0 0.458 ... 3.0 222.0 18.7 394.63 2.94
4 0.06905 0.0 2.18 0.0 0.458 ... 3.0 222.0 18.7 396.90 5.33
.. ... ... ... ... ... ... ... ... ... ... ...
501 0.06263 0.0 11.93 0.0 0.573 ... 1.0 273.0 21.0 391.99 9.67
502 0.04527 0.0 11.93 0.0 0.573 ... 1.0 273.0 21.0 396.90 9.08
503 0.06076 0.0 11.93 0.0 0.573 ... 1.0 273.0 21.0 396.90 5.64
504 0.10959 0.0 11.93 0.0 0.573 ... 1.0 273.0 21.0 393.45 6.48
505 0.04741 0.0 11.93 0.0 0.573 ... 1.0 273.0 21.0 396.90 7.88

[506 rows x 13 columns]
'''
##
'''
CRIM crime rate
ZN density of residential area
INDUS rate of industrial area (non-retail)
CHAS Charles River (1: around the river, 0: others)
NOX NOx concentration
RM average number of rooms par house
AGE rate of houses built before 1940
DIS weighted distance from five employers in Boston
RAD accessibility to major roads
TAX income tax (rates) par $10,000
PTRATIO number of students par teacher
B rate of African Americans 1000(Bk – 0.63)^2
LSTAT rate of low income earners
'''
##
##df = pd.DataFrame(dt.data, columns=dt.feature_names) #data: independent variables
##df['Y'] = dt.target # Y: target/dependent variable is added
###df.to_csv('df.csv', header=True, index=True)

df = pd.read_csv(dfname, index_col=0)
#
#print(df)
#[506 rows x 14 columns]
#
#print(df.columns)
'''
Index(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD', 'TAX',
'PTRATIO', 'B', 'LSTAT', 'Y'],
dtype='object')
'''

########### set Y (dependent variable)
Y = df.eval(yname)
#
#print(Y)
'''
0 24.0
1 21.6
2 34.7
3 33.4
4 36.2
...
501 22.4
502 20.6
503 23.9
504 22.0
505 11.9
Name: Y, Length: 506, dtype: float64
'''

########### set X (independent variables)
if xconv == 'r':
#r: raw X data
print('r: raw X data')
#
##### Raw data X
#
#print("########## Raw Data X ##########")
X = df.drop(yname, axis=1)
Xconv = X # no conversion, but to have the same variable, call X as Xconv
#
#print(Xconv.columns)
'''
Index(['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS', 'RAD', 'TAX',
'PTRATIO', 'B', 'LSTAT'],
dtype='object')
'''
#
#print(Xconv.describe())
'''
CRIM ZN INDUS CHAS ... TAX PTRATIO B LSTAT
count 506.000000 506.000000 506.000000 506.000000 ... 506.000000 506.000000 506.000000 506.000000
mean 3.613524 11.363636 11.136779 0.069170 ... 408.237154 18.455534 356.674032 12.653063
std 8.601545 23.322453 6.860353 0.253994 ... 168.537116 2.164946 91.294864 7.141062
min 0.006320 0.000000 0.460000 0.000000 ... 187.000000 12.600000 0.320000 1.730000
25% 0.082045 0.000000 5.190000 0.000000 ... 279.000000 17.400000 375.377500 6.950000
50% 0.256510 0.000000 9.690000 0.000000 ... 330.000000 19.050000 391.440000 11.360000
75% 3.677082 12.500000 18.100000 0.000000 ... 666.000000 20.200000 396.225000 16.955000
max 88.976200 100.000000 27.740000 1.000000 ... 711.000000 22.000000 396.900000 37.970000

[8 rows x 13 columns]
'''

elif xconv == 's':
X = df.drop(yname, axis=1)
#
#s: standardized X data
print('s: standardized X data')
#
# Standardized data X (average == 0, standard deviation == 1 for all x)
#
scaler = StandardScaler()
scaler.fit(X)
#
#print("########## Standardized Data X ##########")
#print("scaler.fit(X) ->" + str(scaler.fit(X)))
#print("scaler.mean_ ->" + str(scaler.mean_))
#print("scaler.transform ->" + str(scaler.transform(X)))
#
Xconv = scaler.transform(X)
Xconv = pd.DataFrame(Xconv)
#Xconv.columns = boston.feature_names
Xconv.columns = X.columns
#
#print(Xconv.describe())

elif xconv == 'n':
X = df.drop(yname, axis=1)
#
#n: normalized X data
print('n: normalized X data')
#
# Normalized data X (all x are normalized to take values from 0 to 1)
mscaler = MinMaxScaler()
mscaler.fit(X)
#
#print("########## Normalized Data X ##########")
#print("mscaler.fit(X) ->" + str(mscaler.fit(X)))
#print("mscaler.data_max_ ->" + str(mscaler.data_max_))
#print("mscaler.data_range_ ->" + str(mscaler.data_range_))
#print("mscaler.transform ->" + str(mscaler.transform(X)))
#
Xconv = mscaler.transform(X)
Xconv = pd.DataFrame(Xconv)
#Xconv.columns = boston.feature_names
Xconv.columns = X.columns
#
#print(Xconv.describe())
'''
CRIM ZN INDUS CHAS ... TAX PTRATIO B LSTAT
count 506.000000 506.000000 506.000000 506.000000 ... 506.000000 506.000000 506.000000 506.000000
mean 0.040544 0.113636 0.391378 0.069170 ... 0.422208 0.622929 0.898568 0.301409
std 0.096679 0.233225 0.251479 0.253994 ... 0.321636 0.230313 0.230205 0.197049
min 0.000000 0.000000 0.000000 0.000000 ... 0.000000 0.000000 0.000000 0.000000
25% 0.000851 0.000000 0.173387 0.000000 ... 0.175573 0.510638 0.945730 0.144040
50% 0.002812 0.000000 0.338343 0.000000 ... 0.272901 0.686170 0.986232 0.265728
75% 0.041258 0.125000 0.646628 0.000000 ... 0.914122 0.808511 0.998298 0.420116
max 1.000000 1.000000 1.000000 1.000000 ... 1.000000 1.000000 1.000000 1.000000

[8 rows x 13 columns]
'''

else:
print('Speficy X data conversion: r (raw X data), s (standardized X data), or n (normalized X data)')
sys.exit(1) #error status = 1

########## Multiple Linear Regression

clf = linear_model.LinearRegression(fit_intercept=True, normalize=False, copy_X=True, n_jobs=1)
clf.fit(Xconv, Y)
#SGDRegressor
#clf_SGD = linear_model.SGDRegressor(max_iter=500)
#clf_SGD.fit(Xconv, Y)
#
#
smX = sm.add_constant(Xconv)
estX = sm.OLS(Y, smX)
estXfit = estX.fit()
#print(estXfit.summary())
with open('estXfit.summary.txt', 'w') as f:
print(estXfit.summary(), file=f)

########## print out

#print(pd.DataFrame({"Name":Xconv.columns,
# "Coefficients":clf.coef_}).sort_values(by='Coefficients') ) # sorting by coefficients
#print('intercept = ' + str(clf.intercept_)) # intercept
#print('R^2 = ' + str(clf.score(Xconv,Y))) # R^2

with open('clif.txt', 'w') as f:
print(pd.DataFrame({"Name":Xconv.columns,
"Coefficients":clf.coef_}).sort_values(by='Coefficients') , file=f)
print('intercept = ' + str(clf.intercept_), file=f)
print('R^2 = ' + str(clf.score(Xconv,Y)), file=f)

########## plot

plt.figure(1)
plt.title('Multiple Linear Regression')
plt.xlabel(xname, fontsize=14)
plt.ylabel(yname, fontsize=14)

if xconv == 'r':
plt.scatter(Xconv[xname], Y, c='blue', label='Raw Data X')
elif xconv == 's':
plt.scatter(Xconv[xname], Y, c='blue', label='Standardized Data X')
elif xconv == 'n':
plt.scatter(Xconv[xname], Y, c='blue', label='Normalized Data X')
else:
#This section is not executed since exit is done in the previous section.
print('Speficy X data conversion: r (raw X data), s (standardized X data), or n (normalized X data)')
sys.exit(1) #error status = 1

plt.scatter(Xconv.eval(xname), clf.predict(Xconv), c='red', label='Multiple Regression Analysis')
plt.legend(loc='lower right', fontsize=12)
plt.savefig("Figure_Multiple_Linear_Regression_" + xconv + ".png")
plt.show()

########## output data files

#print(X)
#
#print(type(X))
#<class 'pandas.core.frame.DataFrame'>

#print(Xconv)
#
#print(type(Xconv))
#<class 'pandas.core.frame.DataFrame'>

#print(Y)
#print(type(Y))
#<class 'pandas.core.series.Series'>

X_Y = pd.concat([X, Y], axis=1)
Xconv_Y = pd.concat([Xconv, Y], axis=1)

X_Y.to_csv('X_Y.csv', header=True, index=True)
Xconv_Y.to_csv('Xconv_Y.csv', header=True, index=True)

Output Files

**estXfit.summary.txt**
OLS Regression Results ============================================================================== Dep. Variable: Y R-squared: 0.741 Model: OLS Adj. R-squared: 0.734 Method: Least Squares F-statistic: 108.1 Date: Sun, 07 Jun 2020 Prob (F-statistic): 6.72e-135 Time: 07:56:06 Log-Likelihood: -1498.8 No. Observations: 506 AIC: 3026. Df Residuals: 492 BIC: 3085. Df Model: 13 Covariance Type: nonrobust ============================================================================== coef std err t P>\|t\| [0.025 0.975] ------------------------------------------------------------------------------ const 22.5328 0.211 106.814 0.000 22.118 22.947 CRIM -0.9281 0.282 -3.287 0.001 -1.483 -0.373 ZN 1.0816 0.320 3.382 0.001 0.453 1.710 INDUS 0.1409 0.421 0.334 0.738 -0.687 0.969 CHAS 0.6817 0.219 3.118 0.002 0.252 1.111 NOX -2.0567 0.442 -4.651 0.000 -2.926 -1.188 RM 2.6742 0.293 9.116 0.000 2.098 3.251 AGE 0.0195 0.371 0.052 0.958 -0.710 0.749 DIS -3.1040 0.420 -7.398 0.000 -3.928 -2.280 RAD 2.6622 0.577 4.613 0.000 1.528 3.796 TAX -2.0768 0.633 -3.280 0.001 -3.321 -0.833 PTRATIO -2.0606 0.283 -7.283 0.000 -2.617 -1.505 B 0.8493 0.245 3.467 0.001 0.368 1.331 LSTAT -3.7436 0.362 -10.347 0.000 -4.454 -3.033 ============================================================================== Omnibus: 178.041 Durbin-Watson: 1.078 Prob(Omnibus): 0.000 Jarque-Bera (JB): 783.126 Skew: 1.521 Prob(JB): 8.84e-171 Kurtosis: 8.281 Cond. No. 9.82 ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

**cliff.txt**
Name Coefficients 12 LSTAT -3.743627 7 DIS -3.104044 9 TAX -2.076782 10 PTRATIO -2.060607 4 NOX -2.056718 0 CRIM -0.928146 6 AGE 0.019466 2 INDUS 0.140900 3 CHAS 0.681740 11 B 0.849268 1 ZN 1.081569 8 RAD 2.662218 5 RM 2.674230 intercept = 22.532806324110673 R^2 = 0.7406426641094094

**X_Y.csv**
,CRIM,ZN,INDUS,CHAS,NOX,RM,AGE,DIS,RAD,TAX,PTRATIO,B,LSTAT,Y 0,0.00632,18.0,2.31,0.0,0.5379999999999999,6.575,65.2,4.09,1.0,296.0,15.3,396.9,4.98,24.0 1,0.02731,0.0,7.07,0.0,0.469,6.421,78.9,4.9671,2.0,242.0,17.8,396.9,9.14,21.6 2,0.02729,0.0,7.07,0.0,0.469,7.185,61.1,4.9671,2.0,242.0,17.8,392.83,4.03,34.7 3,0.032369999999999996,0.0,2.18,0.0,0.45799999999999996,6.997999999999999,45.8,6.0622,3.0,222.0,18.7,394.63,2.94,33.4 4,0.06905,0.0,2.18,0.0,0.45799999999999996,7.147,54.2,6.0622,3.0,222.0,18.7,396.9,5.33,36.2 5,0.02985,0.0,2.18,0.0,0.45799999999999996,6.43,58.7,6.0622,3.0,222.0,18.7,394.12,5.21,28.7 6,0.08829,12.5,7.87,0.0,0.524,6.0120000000000005,66.6,5.5605,5.0,311.0,15.2,395.6,12.43,22.9 7,0.14455,12.5,7.87,0.0,0.524,6.172000000000001,96.1,5.9505,5.0,311.0,15.2,396.9,19.15,27.1 8,0.21124,12.5,7.87,0.0,0.524,5.631,100.0,6.0821,5.0,311.0,15.2,386.63,29.93,16.5 9,0.17004,12.5,7.87,0.0,0.524,6.004,85.9,6.5921,5.0,311.0,15.2,386.71,17.1,18.9 10,0.22489,12.5,7.87,0.0,0.524,6.377000000000001,94.3,6.3467,5.0,311.0,15.2,392.52,20.45,15.0 11,0.11747,12.5,7.87,0.0,0.524,6.0089999999999995,82.9,6.2267,5.0,311.0,15.2,396.9,13.27,18.9 12,0.09378,12.5,7.87,0.0,0.524,5.888999999999999,39.0,5.4509,5.0,311.0,15.2,390.5,15.71,21.7 13,0.62976,0.0,8.14,0.0,0.5379999999999999,5.949,61.8,4.7075,4.0,307.0,21.0,396.9,8.26,20.4 14,0.6379600000000001,0.0,8.14,0.0,0.5379999999999999,6.096,84.5,4.4619,4.0,307.0,21.0,380.02,10.26,18.2 15,0.62739,0.0,8.14,0.0,0.5379999999999999,5.834,56.5,4.4986,4.0,307.0,21.0,395.62,8.47,19.9 16,1.05393,0.0,8.14,0.0,0.5379999999999999,5.935,29.3,4.4986,4.0,307.0,21.0,386.85,6.58,23.1 17,0.7842,0.0,8.14,0.0,0.5379999999999999,5.99,81.7,4.2579,4.0,307.0,21.0,386.75,14.67,17.5 18,0.80271,0.0,8.14,0.0,0.5379999999999999,5.456,36.6,3.7965,4.0,307.0,21.0,288.99,11.69,20.2 19,0.7258,0.0,8.14,0.0,0.5379999999999999,5.727,69.5,3.7965,4.0,307.0,21.0,390.95,11.28,18.2 20,1.25179,0.0,8.14,0.0,0.5379999999999999,5.57,98.1,3.7979,4.0,307.0,21.0,376.57,21.02,13.6 21,0.8520399999999999,0.0,8.14,0.0,0.5379999999999999,5.965,89.2,4.0123,4.0,307.0,21.0,392.53,13.83,19.6 22,1.2324700000000002,0.0,8.14,0.0,0.5379999999999999,6.142,91.7,3.9769,4.0,307.0,21.0,396.9,18.72,15.2 23,0.9884299999999999,0.0,8.14,0.0,0.5379999999999999,5.813,100.0,4.0952,4.0,307.0,21.0,394.54,19.88,14.5 24,0.75026,0.0,8.14,0.0,0.5379999999999999,5.9239999999999995,94.1,4.3996,4.0,307.0,21.0,394.33,16.3,15.6 25,0.84054,0.0,8.14,0.0,0.5379999999999999,5.599,85.7,4.4546,4.0,307.0,21.0,303.42,16.51,13.9 26,0.67191,0.0,8.14,0.0,0.5379999999999999,5.813,90.3,4.6819999999999995,4.0,307.0,21.0,376.88,14.81,16.6 27,0.9557700000000001,0.0,8.14,0.0,0.5379999999999999,6.047000000000001,88.8,4.4534,4.0,307.0,21.0,306.38,17.28,14.8 28,0.77299,0.0,8.14,0.0,0.5379999999999999,6.495,94.4,4.4547,4.0,307.0,21.0,387.94,12.8,18.4 29,1.00245,0.0,8.14,0.0,0.5379999999999999,6.6739999999999995,87.3,4.239,4.0,307.0,21.0,380.23,11.98,21.0 30,1.13081,0.0,8.14,0.0,0.5379999999999999,5.712999999999999,94.1,4.2330000000000005,4.0,307.0,21.0,360.17,22.6,12.7 31,1.3547200000000001,0.0,8.14,0.0,0.5379999999999999,6.072,100.0,4.175,4.0,307.0,21.0,376.73,13.04,14.5 32,1.38799,0.0,8.14,0.0,0.5379999999999999,5.95,82.0,3.99,4.0,307.0,21.0,232.6,27.71,13.2 33,1.15172,0.0,8.14,0.0,0.5379999999999999,5.7010000000000005,95.0,3.7872,4.0,307.0,21.0,358.77,18.35,13.1 34,1.6128200000000001,0.0,8.14,0.0,0.5379999999999999,6.096,96.9,3.7598,4.0,307.0,21.0,248.31,20.34,13.5 35,0.06417,0.0,5.96,0.0,0.499,5.933,68.2,3.3603,5.0,279.0,19.2,396.9,9.68,18.9 36,0.09744,0.0,5.96,0.0,0.499,5.841,61.4,3.3779,5.0,279.0,19.2,377.56,11.41,20.0 37,0.08014,0.0,5.96,0.0,0.499,5.85,41.5,3.9342,5.0,279.0,19.2,396.9,8.77,21.0 38,0.17505,0.0,5.96,0.0,0.499,5.966,30.2,3.8473,5.0,279.0,19.2,393.43,10.13,24.7 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**Xconv_Y.csv**
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Figures

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The Financial Journal (Global)

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Saturday, June 6, 2020

Multiple Linear Regression of Raw Data, Standardized Data, and Normalized Data

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Deep Learning (Regression, Multiple Features/Explanatory Variables, Supervised Learning): Impelementation and Showing Biases and Weights

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