Linear Regression with Simulated Data - Solution code (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

100 Random Sample from a Normal Distribution (np.random.randn)

X = np.random.randn(100)
X

array([-0.86263111,  2.12205253, -0.19119369,  0.8914565 , -0.06863318,
       -1.85375508, -0.68943993,  1.20195946, -0.70193827,  1.36462236,
       -2.9584875 ,  0.11704817, -1.9234075 ,  1.49977632, -0.30407317,
       -0.39180849,  0.70300464,  0.86246528, -0.42644705,  0.17636177,
       -1.7870432 , -0.00659526, -1.22431819,  0.43125762,  0.61653442,
        0.54664429, -0.35557064, -0.65142241,  0.89569784, -1.00710185,
        0.81701861, -0.12796308,  0.62462281,  0.15555161, -1.33867444,
        0.40105962, -0.85043252,  1.05851956, -0.65293783, -0.17681899,
        0.27571891,  0.62521257,  0.360203  , -2.48734398,  1.43893884,
       -0.7958003 , -0.23526785,  1.05522751,  0.20748649,  0.41079423,
       -1.49319904,  1.54552729, -0.29076506,  0.68255727, -1.78297863,
        0.95463271, -0.19981706,  1.22516288, -1.07704283,  0.82060848,
       -1.29910111, -0.06732896, -1.06124267, -0.23629949,  2.09987858,
       -1.26369429,  0.03237696, -0.98521614,  0.40883493, -0.91302624,
        0.67147181, -0.5961868 ,  1.17592021,  0.52573888, -1.29840116,
        1.20059359, -1.28642861,  1.04867606,  0.37315101,  0.91649244,
       -1.79039163, -0.48341874, -1.31889581,  0.09449798,  0.15883817,
        0.82490546, -0.72970416,  0.69012513, -0.59388906, -0.01855135,
       -1.05276867,  0.3757267 ,  0.17818673,  0.72823495,  1.83242879,
       -1.88055631,  1.03954104,  0.89407288,  0.22923608, -0.15309013])

Define our Betas and Generate Y

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

array([-0.09811801,  8.02864696,  3.24355683,  1.75900294,  2.54227678,
       -3.47200938,  0.49449328,  6.67594284,  0.0339692 ,  5.85778502,
       -7.52520879,  1.38200135, -3.64759611,  7.63016788,  0.68603627,
        1.36268951,  4.69130299,  4.75749854, -0.15151476,  3.75743203,
       -5.01325723,  1.12629783, -1.186844  ,  3.93319805,  4.34085286,
        3.05672638,  1.21419111,  0.27384927,  5.2467575 , -2.09259539,
        3.41953313,  3.16552732,  4.74774104,  1.45897499, -2.61878716,
        2.39699893, -0.85819949,  3.67022824,  0.14642679,  0.58831642,
        1.51824758,  3.1234011 ,  3.40939318, -4.07842134,  4.85469464,
       -0.74881077, -0.30103399,  4.88824007,  4.95694325,  4.87147428,
       -1.92303363,  6.36813992,  1.02471249,  4.50099746, -3.57528305,
        4.40479345,  0.5772572 ,  4.95837754, -0.48444755,  4.79863027,
       -1.97436127,  0.41789391, -2.64062232,  1.06697885,  8.96919591,
       -1.24571585,  4.39552265, -0.77589849,  4.08719976,  0.40992796,
        5.40443798,  1.7045144 ,  4.59977162,  3.25447816, -2.61355147,
        8.08419741, -2.10114368,  5.75478627,  4.57216778,  4.6388713 ,
       -2.99941236,  0.94046493, -1.81890935,  1.59313132,  1.21986292,
        5.44534611,  1.05335039,  3.00261338,  0.78057142,  1.9315195 ,
       -0.23510765,  2.74030914,  3.85861009,  4.85470511,  8.03524818,
       -1.29306121,  6.31443079,  4.73268197,  2.21379844,  0.79977881])

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)
results = model.fit()
results.summary()

Plot with Seaborn

sns.lmplot(x="X",y='Y',data=df)

<seaborn.axisgrid.FacetGrid at 0x2d83be058d0>