Linear Regression with Simulated Data - (done).ipynb

Kernel: Python 3

Linear Regression with Simulated Data

## Basic imports
%matplotlib inline
import numpy as np
import pandas as pd
import seaborn as sns
import statsmodels.formula.api as smf

Generate a Sample of Size 100 from a Normal Distribution (np.random.randn)

X = np.random.randn(100) #n for normal
X

array([ 0.06493375,  0.7984497 ,  0.51634406, -0.17006532,  0.67659552,
       -0.12039165,  1.05648162, -0.04658388,  0.12489761,  1.10119439,
       -1.79839814,  0.10490968,  1.57167251, -0.53698783, -1.16232652,
        0.84850172,  1.30612834,  0.59375966, -0.52700669,  0.11570846,
       -0.47324893, -0.48848682,  1.43785741,  0.18378832,  0.66465429,
        0.2448326 , -1.44672557,  0.34443231, -0.3575056 ,  0.37252765,
       -0.3071095 , -0.09579139,  1.02151853,  0.48536062, -2.32451609,
       -0.15650236, -1.05341782, -0.69982228, -1.10457518, -0.91441854,
        0.49910147, -0.29526662, -1.52812187, -0.08339499,  0.19289274,
        0.39515657,  1.85071214,  1.3542823 , -0.05058901, -0.92227413,
        1.49603742, -0.32747489, -1.19727926, -0.23266561, -1.15589619,
       -0.77248483, -0.49974948,  0.13588953, -0.89503119,  1.72353011,
        0.68029549,  0.84034493,  0.10852891,  0.22685788,  0.38786926,
        0.71066973, -0.12920315,  0.04409544, -0.60161435, -0.91400097,
       -0.19600274,  0.34592439, -0.15931562,  0.28707037,  0.64155796,
       -0.34302668, -0.54639181, -2.85667605,  2.24233233, -0.48903869,
        0.13769365, -0.60268568,  0.40513136,  0.59576328,  0.54502947,
       -0.20575235,  0.61441866,  0.77973282, -0.09726794, -0.27554759,
       -0.05035097, -0.58245879,  2.34022181, -1.72706398,  0.92324506,
        1.29250059,  0.05048737,  0.0044817 , -0.51776128, -1.02294188])

Define our Betas and Generate Y

beta_0 = 2
beta_1 = 3
Y = beta_0 + beta_1*X + np.random.randn(100)
Y

array([ 2.20400099,  3.94138477,  3.10202787,  3.2208578 ,  4.11947607,
        2.94827028,  6.39627038,  1.62492766, -0.29631979,  4.24975102,
       -2.04639204,  2.43215487,  8.20655562,  1.23559254, -2.09947287,
        4.54849702,  7.25724375,  3.0863531 ,  0.65963968,  1.83513297,
        0.44139728,  1.00096155,  7.45235381,  1.95085381,  4.84431035,
        2.0972651 , -1.61514519,  1.84685114,  2.30036601,  4.04030607,
        1.5794858 ,  3.83703922,  4.51567908,  2.86940751, -6.73865171,
        2.74605363, -0.21813694,  2.03561071, -2.89354033, -0.79323186,
        3.95558333,  0.68928368, -3.83102513,  1.55405958,  1.12117538,
        3.1964302 ,  7.94143169,  4.17339876,  2.73823142, -1.19459812,
        5.88300785,  0.01978937, -0.18083988, -0.78939549, -0.19297022,
        0.21102042,  0.44735634,  2.53348305, -1.49476516,  7.63960977,
        4.77217487,  4.23736443,  3.48669396,  1.61068156,  2.60711488,
        2.86067989,  1.42062426,  2.12219028, -0.36938175, -0.35855762,
        1.94387742,  3.90748891,  1.05681304,  3.38315959,  3.39337211,
        2.30845007,  1.9072533 , -7.09003809,  7.78038171,  2.44615193,
        3.76694585,  0.66574515,  2.87776588,  5.03432225,  3.07695276,
        1.70177004,  3.4697147 ,  3.74098472,  2.01271124,  3.33540658,
        2.31107535,  0.29698396,  8.00897885, -2.83864825,  3.87985048,
        5.07064712,  2.68973698,  3.42341515,  2.1819507 , -1.20161521])

Throw into a Data Frame for Easy processing

df = pd.DataFrame({'X': X, 'Y':Y})
df.head()

Generate Model and Look at the results`

model = smf.ols(formula='Y~X', data=df) #predict Y given X
results = model.fit()
results.summary()

Plot with Seaborn

sns.lmplot(x="X",y='Y',data=df) #seaborn way to plot a regression

<seaborn.axisgrid.FacetGrid at 0x10b787f98>