Using 'statistics' module
In [2]:
DataSet = [13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 36, 40, 45, 46, 52, 70]
# Sum of all elements using simple built in sum function
print("Sum of all items of Data Set : " + str(sum(DataSet)))
# Getting Count of each items using counter collection
"""
Counter is an unordered collection where elements are stored as Dict keys and their count as dict value
"""
from collections import Counter
print("Count of each items in Data Set : ")
print(Counter(DataSet))
# Use of statistics module
import statistics as st
# Mean -> Sum of all data items / total no of data items
print("Mean of Data Set : ")
print(st.mean(DataSet))
# Median -> Average of two items exist in mid of data set
print("Median of Data Set : ")
print(st.median(DataSet))
# Mode -> Item with highest frequency of appearance
print("Mode of Data Set : ")
print(st.mode(DataSet))
# Mid-range -> Average of MaxVale And MinValue item
print("Mid Range Value Of Data Set : ")
print(st.mean([max(DataSet), min(DataSet)]))
# Other Useful statistical measures
print("Quantiles Of Data Set : ")
print(st.quantiles(data = DataSet, n = 4)) # [20.0, 25.0, 35.25]
print("Std. Deviation Of Data Set : ")
print(st.stdev(DataSet))
print("Variance Of Data Set : ")
print(st.variance(DataSet))
Sum of all items of Data Set : 774
Count of each items in Data Set :
Counter({25: 4, 35: 3, 16: 2, 20: 2, 22: 2, 33: 2, 13: 1, 15: 1, 19: 1, 21: 1, 30: 1, 36: 1, 40: 1, 45: 1, 46: 1, 52: 1, 70: 1})
Mean of Data Set :
29.76923076923077
Median of Data Set :
25.0
Mode of Data Set :
25
Mid Range Value Of Data Set :
41.5
Quantiles Of Data Set :
[20.0, 25.0, 35.25]
Std. Deviation Of Data Set :
13.158442741624686
Variance Of Data Set :
173.14461538461538
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In [3]:
import pandas as pd
In [4]:
df = pd.read_csv('HeightWeight.csv')
In [5]:
df.head()
Out[5]:
| Index | Height(Inches) | Weight(Pounds) | |
|---|---|---|---|
| 0 | 1 | 65.78331 | 112.9925 |
| 1 | 2 | 71.51521 | 136.4873 |
| 2 | 3 | 69.39874 | 153.0269 |
| 3 | 4 | 68.21660 | 142.3354 |
| 4 | 5 | 67.78781 | 144.2971 |
'statistics' is a core Python package. We can use it but now list it. !pip show statistics WARNING: Package(s) not found: statistics
In [8]:
st.correlation(df['Height(Inches)'], df['Weight(Pounds)'])
Out[8]:
0.5028585206028441
Linear Regression¶
In [6]:
# New in version 3.10
slope, intercept = st.linear_regression(df['Height(Inches)'], df['Weight(Pounds)'])
In [7]:
slope, intercept
Out[7]:
(3.0834764454029657, -82.57574306454092)
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Using 'statsmodels' module
In [8]:
!pip show statsmodels
Name: statsmodels Version: 0.13.5 Summary: Statistical computations and models for Python Home-page: https://www.statsmodels.org/ Author: Author-email: License: BSD License Location: /home/ashish/anaconda3/envs/py310/lib/python3.10/site-packages Requires: numpy, packaging, pandas, patsy, scipy Required-by:
In [9]:
# Calculating various statistics value for a data set using statmodels , sciPy , numpy and pandas module functions
# importing required modules
from statsmodels import stats
import statsmodels.stats.weightstats as ws
import statsmodels.stats.descriptivestats as ds
import statsmodels.stats.libqsturng as lq
In [10]:
DataSet = [13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 36, 40, 45, 46, 52, 70]
In [11]:
mean = ws.stats.gmean(DataSet)
print(mean)
# median = ws.stats.median(DataSet)
# AttributeError: module 'scipy.stats' has no attribute 'median'
desc_stats = ds.describe(DataSet)
print("desc_stats using statsmodels : ", desc_stats)
27.347117200207276 desc_stats using statsmodels : 0 nobs 26.000000 missing 0.000000 mean 29.769231 std_err 2.580583 upper_ci 34.827080 lower_ci 24.711381 std 13.158443 iqr 14.750000 iqr_normal 10.934191 mad 10.213018 mad_normal 12.800120 coef_var 0.442015 range 57.000000 max 70.000000 min 13.000000 skew 1.206785 kurtosis 4.506284 jarque_bera 8.768727 jarque_bera_pval 0.012471 mode 25.000000 mode_freq 0.153846 median 25.000000 1% 13.500000 5% 15.250000 10% 16.000000 25% 20.250000 50% 25.000000 75% 35.000000 90% 45.500000 95% 50.500000 99% 65.500000
In [12]:
type(desc_stats) # pandas.core.frame.DataFrame
Out[12]:
pandas.core.frame.DataFrame
In [16]:
for i in ['mean', 'median', 'mode', 'std', '25%', '50%', '75%',
'iqr', 'min', 'max']:
print(i, desc_stats.loc[i][0])
mean 29.76923076923077 median 25.0 mode 25.0 std 13.158442741624686 25% 20.25 50% 25.0 75% 35.0 iqr 14.75 min 13.0 max 70.0
In [14]:
import pandas as pd
mean = pd.Series(DataSet).describe()
print("Mean using pandas :", mean)
Mean using pandas : count 26.000000 mean 29.769231 std 13.158443 min 13.000000 25% 20.250000 50% 25.000000 75% 35.000000 max 70.000000 dtype: float64
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Linear Regression¶
In [19]:
import statsmodels.api as sm
import pandas as pd
In [20]:
df = pd.read_csv('HeightWeight.csv')
In [21]:
results = sm.OLS(df['Height(Inches)'], df['Weight(Pounds)']).fit()
In [23]:
results.summary()
Out[23]:
| Dep. Variable: | Height(Inches) | R-squared (uncentered): | 0.993 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared (uncentered): | 0.993 |
| Method: | Least Squares | F-statistic: | 3.783e+06 |
| Date: | Mon, 15 May 2023 | Prob (F-statistic): | 0.00 |
| Time: | 13:09:01 | Log-Likelihood: | -78144. |
| No. Observations: | 25000 | AIC: | 1.563e+05 |
| Df Residuals: | 24999 | BIC: | 1.563e+05 |
| Df Model: | 1 | ||
| Covariance Type: | nonrobust |
| coef | std err | t | P>|t| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| Weight(Pounds) | 0.5313 | 0.000 | 1944.918 | 0.000 | 0.531 | 0.532 |
| Omnibus: | 3.114 | Durbin-Watson: | 1.974 |
|---|---|---|---|
| Prob(Omnibus): | 0.211 | Jarque-Bera (JB): | 3.091 |
| Skew: | 0.024 | Prob(JB): | 0.213 |
| Kurtosis: | 3.025 | Cond. No. | 1.00 |
Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
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