# Week4

## Linear regression

```python
gradient,intercept,r_value, p_value, 
stderr=scipy.stats.linregress(x,y)
```

## Polynomial regression

```python
np.polynomial.polynomial.polyfit
c,stats=nppp.polyfit(x,y,degree,full=True, w=None)
nppp.polyval(datasample,c)
```

## Clustering: kmeans/kmeans2

```python
centroids,var=scipy.cluster.vq.kmeans(Dataset, Number_of_Clusters)
id,dis=scipy.cluster.vq.vq(Dataset, centroids)
np.random.multivariate_normal([10,0],[[3,1],[1,4]]),size=[100,1])
```

## Exercise

### 1-. Import the ‘Auto Insurance in Sweden’ dataset from the following url, and do a linear regression to fit the data. Plot the data and the regression line.

url: <https://www.math.muni.cz/~kolacek/docs/frvs/M7222/data/AutoInsurSweden.txt>

```python
import pandas as pd
import numpy as np
import numpy.polynomial.polynomial as nppp
import scipy.stats as sps
from pylab import plot,show
DataFrame = pd.read_csv('C:/Users/MA/Desktop/Insurance.csv',header=None)
DataMatrix = DataFrame.as_matrix()
InputMatrix= np.array(DataMatrix[:,0])
OutMatrix = np.array(DataMatrix[:,1])
(gradient,intercept,rvalue,pvalue,stderr) = sps.linregress(InputMatrix,OutMatrix)
Regression_line = nppp.polyval(InputMatrix,[intercept,gradient])
print ("Gradient & Intercept", gradient, intercept)
plot(InputMatrix,OutMatrix, 'vr')
plot(InputMatrix,Regression_line ,'b.-')
show()
```

### 2 - Download the ‘IRIS’ dataset from the url below, import it to Python and do a 3-mean clustering based on the inputs (4-dimesnion). Plot the members of each cluster with different colour (Red, Blue & Green ) in a 2-axis coordinate which the horizontal axis is the first input and the vertical one is second input.

url: <https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data>

```python
import pandas as pd
import numpy as np
from scipy.cluster.vq import kmeans,vq
from pylab import 
DataFrame = pd.read_csv('C:/Users/MA/Desktop/iris.csv',header=None)
DataMatrix = DataFrame.as_matrix()
InputMatrix = np.matrix(DataMatrix[:,:4])
centroids,_ = kmeans(InputMatrix,3)
id,_ = vq(InputMatrix,centroids)
print(centroids)
print(id)
plot(InputMatrix[id==0,0],InputMatrix[id==0,1],'*b',InputMatrix[id==
1,0],InputMatrix[id==1,1],'vr',InputMatrix[id==2,0],InputMatrix[id==
2,1],'og',linewidth=5.5)
show()
```


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