Title :¶
Exercise: Beta Values for Data from Random Universe
Description :¶
Given a RandomUniverse(dataframe)->dataframe function that gives a new dataset from a "parallel" universe, calculate the $\beta_0$'s and $\beta_1$'s and plot a histogram like the one below.
Data Description:¶
Instructions:¶
- Get a new dataframe using the RandomUniverse function already provided in the exercise
- Calculate $\beta_0$, $\beta_1$ for that particular dataframe
- Add the calculated $\beta_0$ and $\beta_1$ values to a python list
- Plot a histogram using the lists calculated above
Hints:¶
$${\widehat {\beta_1 }}={\frac {\sum _{i=1}^{n}(x_{i}-{\bar {x}})(y_{i}-{\bar {y}})}{\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}}}$$$${\widehat {\beta_0 }}={\bar {y}}-{\widehat {\beta_1 }}\,{\bar {x}}$$plt.subplots() Create a figure and a set of subplots
ax.hist() Plot a histogram from a list or series.
In [1]:
# Import necessary libraries
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from randomuniverse import RandomUniverse
%matplotlib inline
In [2]:
# Read the advertising dataset as a pandas dataframe
df = pd.read_csv('Advertising_adj.csv')
# Take a quick look at the dataframe
df.head()
Out[2]:
| tv | sales | |
|---|---|---|
| 0 | 230.1 | 465.26 |
| 1 | 44.5 | 218.95 |
| 2 | 17.2 | 195.79 |
| 3 | 151.5 | 389.47 |
| 4 | 180.8 | 271.58 |
In [10]:
# Create two empty lists that will store the beta values
beta0_list, beta1_list = [],[]
# Choose the number of "parallel" Universes to generate
# that many new versions of the dataset
parallelUniverses = 10000
# Loop over the maximum number of parallel Universes
for i in range(parallelUniverses):
# Call the RandomUniverse helper function with the dataframe
# read from the data file
df_new = RandomUniverse(df)
# Find the mean of the predictor values i.e. tv
xmean = df_new.tv.mean()
# Find the mean of the response values i.e. sales
ymean = df_new.sales.mean()
# Compute the analytical values of beta0 and beta1 using the
# equation given in the hints
beta1 = np.sum((df_new.tv-xmean) * (df_new.sales-ymean)) / np.sum((df_new.tv-xmean)**2)
beta0 = ymean-beta1*xmean
# Append the calculated values of beta1 and beta0 to the appropriate lists
beta0_list.append(beta0)
beta1_list.append(beta1)
In [11]:
### edTest(test_beta) ###
# Compute the mean of the beta values
beta0_mean = np.mean(beta0_list)
beta1_mean = np.mean(beta1_list)
In [12]:
# Plot histograms of beta_0 and beta_1 using lists created above
fig, ax = plt.subplots(1,2, figsize=(18,8))
ax[0].hist(beta0_list)
ax[1].hist(beta1_list)
ax[0].set_xlabel('Beta 0')
ax[1].set_xlabel('Beta 1')
ax[0].set_ylabel('Frequency');
Out[12]:
Text(0, 0.5, 'Frequency')
In [13]:
### edTest(test_chow1) ###
# Submit an answer choice as a string below
# (Eg. if you choose option C, put 'C')
answer1 = 'D'
In [0]: