# Pseudo Facebook Data - Exploring Two Variables

In this section, we will be re-using the data from the previous post based on Pseudo Facebook data from udacity.

The data from the project corresponds to a typical data set
at Facebook.
You can load the data through the following command. Notice that this is a TAB delimited *csv* file.
This data set consists of 99000 rows of data. We will see the details of different columns using the
command below.

```
import pandas as pd
import numpy as np
#Read csv file
pf = pd.read_csv("https://s3.amazonaws.com/udacity-hosted-downloads/ud651/pseudo_facebook.tsv", sep = '\t')
cats = ['userid', 'dob_day', 'dob_year', 'dob_month']
for col in pf.columns:
if col in cats:
pf[col] = pf[col].astype('category')
#summarize data
pf.describe(include='all', percentiles=[]).T.replace(np.nan,' ', regex=True)
```

Usually, it is best to use a scatter plot to analyze two variables:

```
import matplotlib.pyplot as plt
import seaborn as sns
sns.set(style="darkgrid")
%matplotlib inline
```ax = sns.regplot(x='age', y='friend_count', data=pf, fit_reg=False)
plt.xlim(13, 90)
plt.ylim(0,5000)

We can notice some really interesting behavior in the ugly scatter plot above:

- The age data is binned, as expected (only integers allowed)
- Young people around the age of 20 have maximum friend count.
- There is unusual spike in friends count of people aged more than 100. This could mostly be some flaw in the data, probably based on incorrect entry by the users.
- People around the age of 70 too have quite a large amount of friends. This is pretty interesting and could point to the use of the social media site by an unexpected group of people.

We can use summary command to find the bounds on age and then use that to limit age axis.

```
pf.age.describe()
```

Furthermore, we notice at some areas of the plot being too dense, where as some to be really sparse. The areas where points are too dense is called “over plotting” - It is impossible to extract any meaningful statistics from this region.
In order to overcome this, we can set the transparency of the plots using the alpha parameter in the plt.scatter() method. Using a value of ^{1}⁄_{20} means, one point that will plotted will be equal to 20 original points.

```
ax = sns.regplot(x='age', y='friend_count', data=pf, fit_reg=False, color='green', scatter_kws={'alpha': 0.05})
plt.xlim(13, 90)
plt.ylim(0,5000)
plt.plot([13, 90], [600, 600], linewidth=2, color='r')
```

Based on these new plots, we can find bulk of higher friend count for younger people is still less than 600. We still find higher count for age group of 70.

Furthermore, we can do a better representation of data using the coord_trans() method. We will be using a square root function.

In order to that, we will first create an “sqrt” scale.

```
import numpy as np
from numpy import ma
from matplotlib import scale as mscale
from matplotlib import transforms as mtransforms
from matplotlib.ticker import AutoLocator
```class SqrtScale(mscale.ScaleBase):
"""
Scales data using np.sqrt method.

The scale function:
np.sqrt(x)

The inverse scale function:
x**2
"""

# The scale class must have a member ``name`` that defines the
# string used to select the scale. For example,
# ``gca().set_yscale("mercator")`` would be used to select this
# scale.
name = 'sqrt'
def __init__(self, axis):
"""
Any keyword arguments passed to ``set_xscale`` and
``set_yscale`` will be passed along to the scale's
constructor.
"""
mscale.ScaleBase.__init__(self)
def get_transform(self):
"""
Override this method to return a new instance that does the
actual transformation of the data.
The SqrtTransform class is defined below as a
nested class of this one.
"""
return self.SqrtTransform()
def set_default_locators_and_formatters(self, axis):
"""
Override to set up the locators and formatters to use with the
scale.
"""
axis.set_major_locator(AutoLocator())
class SqrtTransform(mtransforms.Transform):
# There are two value members that must be defined.
# ``input_dims`` and ``output_dims`` specify number of input
# dimensions and output dimensions to the transformation.
# These are used by the transformation framework to do some
# error checking and prevent incompatible transformations from
# being connected together. When defining transforms for a
# scale, which are, by definition, separable and have only one
# dimension, these members should always be set to 1.
input_dims = 1
output_dims = 1
is_separable = True
def __init__(self):
mtransforms.Transform.__init__(self)
def transform_non_affine(self, a):
"""
This transform takes an Nx1 ``numpy`` array and returns a
transformed copy.
"""
return np.sqrt(a)
def inverted(self):
"""
Override this method so matplotlib knows how to get the
inverse transform for this transform.
"""
return SqrtScale.InvertedSqrtTransform()
class InvertedSqrtTransform(mtransforms.Transform):
input_dims = 1
output_dims = 1
is_separable = True
def __init__(self):
mtransforms.Transform.__init__(self)
def transform_non_affine(self, a):
return a**2
def inverted(self):
return SqrtScale.SqrtTransform()
# Now that the Scale class has been defined, it must be registered so
# that `matplotlib`

can find it.
mscale.register_scale(SqrtScale)

```
fig, ax = plt.subplots()
fig.set_size_inches(8.6, 6.4)
ax = sns.regplot(x='age', y='friend_count', data=pf, fit_reg=False, color='cyan', scatter_kws={'alpha': 0.05}, ax=ax)
plt.xlim(13, 90)
plt.ylim(0,4599)
plt.yscale('sqrt')
plt.plot([13, 90], [600, 600], linewidth=2, color='r')
```

On a similar way, we can look at relationship between friends initiated and age.

```
fig, ax = plt.subplots()
fig.set_size_inches(8.6, 6.4)
kws = {'alpha': 0.05}
ax = sns.regplot(x='age', y='friendships_initiated', data=pf, fit_reg=False, color='purple', scatter_kws=kws, ax=ax)
plt.xlim(13, 90)
plt.ylim(0,4599)
plt.yscale('sqrt')
```

Interestingly, we find this distribution to be very similar to the one for friend count.

Scatter plots try to keep us very close to the data. It represents each and every data point. However, in order to judge the quality of a data, it is important to know its important statistics like mean, median etc. How does average of a variable vary *wrt* to the some other variable.

We want to say, study how does average friend count vary with age. In order to study this we will use the grouping properties of pandas module.

First we want to group our data frame by age. Then, we can create a new data frame that lists friend count mean, median and frequency (n) by using first the groupby() and then using the agg() method. We can look at first few data points of this new data frame using the head() method.

```
def groupByStats(pf, groupCol, statsCol):
''' return a dataframe with groupByCol'''
# Define the aggregation calculations
aggregations = {
statsCol: {
(statsCol+'_mean'): 'mean',
(statsCol+'_median'): 'median',
(statsCol+'_q25'): lambda x: np.percentile(x,25),
(statsCol+'_q75'): lambda x: np.percentile(x,75),
'n': 'count'/div>
}
}
pf_group_by_age = pf.groupby(groupCol, as_index=False).agg(aggregations).rename(columns = {'':groupCol})
pf_group_by_age.columns = pf_group_by_age.columns.droplevel()
return pf_group_by_age
pf_group_by_age = groupByStats(pf, 'age', 'friend_count')
pf_group_by_age.head(20)
```

Now, let us look at this new data frame visually. We can first look at the relationship between average friend count and age.

```
pf_group_by_age.plot(x='age', y='friend_count_mean', legend=False)
plt.ylabel("Friend Count Mean")
```

We can use this plot as good summary of the original scatter plot and put the two on top of each other.

```
ax = sns.regplot(x='age', y='friend_count', data=pf, fit_reg=False, color='cyan', x_jitter=0.5, y_jitter=1.0, scatter_kws={'alpha': 0.05})
pf_group_by_age.plot(x='age', y='friend_count_q25', ax=ax, color='red', style='–')
pf_group_by_age.plot(x='age', y='friend_count_median', ax=ax, color='blue')
pf_group_by_age.plot(x='age', y='friend_count_mean', ax=ax, color='green', style='–')
pf_group_by_age.plot(x='age', y='friend_count_q75', ax=ax, color='red')
plt.xlim(13, 70)
plt.ylim(0,1000)
plt.ylabel("Friend Count")
```

In the above plot, we can see that between the age group 30-69, 75% of population has less than 200 friends.

In stead of using 4 different summary measures to analyze the above data, we can use a single number!

Often analysts will use correlation coefficients to summarize this. We will use the Pearson product moment correlation ®. You can look at the pandas corr() method for details. This measures a linear correlation between two variables.

```
df = pf[(pf['age'] < 70) & (pf['age'] >= 13)]
df['age'].corr(df['friend_count'], method='pearson')
```

We can also have other measures of relationship. For example, a measure of monotonic relationship would be done using Spearman coefficient. Similarly, a measure of strength of dependence between two variables can be done using the “Kendall Rank Coefficient”. A more detailed description about these can be found at http://www.statisticssolutions.com/correlation-pearson-kendall-spearman/.

We will now look at variables that are strictly correlated using scatter plots.

One such example in our dataset would be a relationship between likes_received (y) vs. www_likes_received (x).

```
ax = sns.regplot(x='www_likes_received', y='likes_received', data=pf, color='cyan', ci=None, line_kws={'color': 'red'})
plt.xlim(0, np.percentile(pf.www_likes_received, 95))
plt.ylim(0, np.percentile(pf.likes_received, 95))
```

We have used numpy percentile() method to find upper limits of x and y data. Additionally, we added a correlation line using the regplot().

We can find the numerical value of the correlation between these two variables.

```
pf['www_likes_received'].corr(pf['likes_received'], method='pearson')
```

Correlation between two variables might not be a good thing always. For example in the above case, it was simply due to the artifact of the two data sets were highly coupled, one was a super set of the other.

Let us take a look again at the modified data frame created using the groupby methods. In particular, we want to remove any noise in the average values.

```
pf['age_with_months'] = pf.age + (12-pf.dob_month)/12
pf_group_by_age_with_months = groupByStats(pf, 'age_with_months', 'friend_count')
pf1 = pf_group_by_age[pf_group_by_age['age'] < 71]
pf2 = pf_group_by_age_with_months[pf_group_by_age_with_months['age_with_months'] < 71]
```

```
f, (ax1, ax2, ax3) = plt.subplots(3)
f.set_size_inches(9, 9)
sns.regplot(x='age_with_months', y='friend_count_mean', data=pf2, scatter=False, lowess=True, ci=95, line_kws={'color': 'red'}, ax=ax1)
pf2.plot(x='age_with_months', y='friend_count_mean', legend=False, ax=ax1)
ax1.set_xlim([13, 71])
```sns.regplot(x='age', y='friend_count_mean', data=pf1, scatter=False, lowess=True, ci=95, line_kws={'color': 'green'}, ax=ax2)
pf1.plot(x='age', y='friend_count_mean', legend=False, ax=ax2)
ax2.set_xlim([13, 71])

pf11 = pf1.copy()
pf11['ageRounded'] = np.round(pf1['age']/5.0)*5.0
sns.regplot(x='ageRounded', y='friend_count_mean', data=pf11, scatter=False, lowess=True, ci=95, line_kws={'color': 'cyan'}, ax=ax3)
pf11.plot(x='ageRounded', y='friend_count_mean', legend=False, ax=ax3)
ax3.set_xlim([13, 71])

This is an example of bias variance trade off, and is similar to the trade off we make when choosing the bin width in histograms. One way, we can do this quite easily in seaborn is using the lowess option, however, in the current implementation it fails to provide any error estimate on the fitted regression!

Lowess option in the seaborn library uses Loess and Lowess method for smoothing. Here, the model is based on the idea that data is continuous and smooth.

So, through this post, we have noticed several ways to plot the same data. The obvious that arises is which plot to choose? In EDA, however, answer to this is, simply you should choose. The idea in EDA is that the same data when plotted differently, glean different incites.