Commit 0473dcd0 authored by Maximilian Vitz's avatar Maximilian Vitz
Browse files

Week1 Lecture added.

parent 3c650424
%% Cell type:markdown id: tags:
<div>
<img src="IIIPIB_RWTH.png" style="float: right;height: 6.5em;">
</div>
## Statistics and Data Analysis (WS 2021)
**Jörg Pretz**
%% Cell type:code id: tags:
``` python
import numpy as np
import matplotlib.pyplot as plt
```
%% Cell type:markdown id: tags:
## Mean and Standard deviation
%% Cell type:code id: tags:
``` python
x=[177,186,181,198,165,156,176]
mean=np.mean(x)
std=np.std(x)
print(mean,std)
```
%%%% Output: stream
177.0 12.671678206592393
%% Cell type:markdown id: tags:
### Calculate standard deviation by hand
%% Cell type:code id: tags:
``` python
x=np.array(x) # convert from list to array in order manipulate x
x2= np.mean(x**2)
std1 = np.sqrt(x2- mean**2)
std1
```
%%%% Output: execute_result
12.67167820659235
%% Cell type:markdown id: tags:
## Correlations
%% Cell type:code id: tags:
``` python
x=[1,2,3,4]
y=[1.1,1.9,3.2,3.9]
plt.scatter(x,y)
```
%%%% Output: execute_result
<matplotlib.collections.PathCollection at 0x7fb0c1a16c70>
%%%% Output: display_data
![](data:image/png;base64,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)
%% Cell type:code id: tags:
``` python
cov=np.cov(x,y)
print(cov)
```
%%%% Output: stream
[[1.66666667 1.61666667]
[1.61666667 1.58916667]]
%% Cell type:markdown id: tags:
## Correlation coefficient
%% Cell type:code id: tags:
``` python
rho = cov[0][1]/np.sqrt(cov[0][0]*cov[1][1])
print(rho)
```
%%%% Output: stream
0.9933707902922091
%% Cell type:code id: tags:
``` python
y1=-np.array(y)
cov=np.cov(x,y1)
rho = cov[0][1]/np.sqrt(cov[0][0]*cov[1][1])
rho
```
%%%% Output: execute_result
-0.9933707902922091
%% Cell type:code id: tags:
``` python
plt.scatter(x,y1)
```
%%%% Output: execute_result
<matplotlib.collections.PathCollection at 0x7fb0c198ffa0>
%%%% Output: display_data
![](data:image/png;base64,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)
%% Cell type:code id: tags:
``` python
```
%% Cell type:markdown id: tags:
<div>
<img src="IIIPIB_RWTH.png" style="float: right;height: 6.5em;">
</div>
## Statistics and Data Analysis (WS 2021)
**Jörg Pretz**
%% Cell type:code id: tags:
``` python
```
%% Cell type:code id: tags:
``` python
```
......
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