## Linear Regression example with NumPy

```
import csv
import matplotlib.pyplot as plt
import numpy as np
def representsInt(s):
try:
int(s)
return True
except ValueError:
return False
# Load training data
with open('train.csv') as f:
dataset = [{k: int(v) if representsInt(v) else v for k, v in row.items()}
for row in csv.DictReader(f, skipinitialspace=True)]
# Simple data scaling without normalization
for i in range(0, len(dataset)):
dataset[i]['SalePrice'] = dataset[i]['SalePrice']/1000
feature = 'TotalBsmtSF' # What we provide
target = 'SalePrice' # What we look for
# Cost function
def cost():
global dataset
errorTotal = 0
for item in dataset:
errorTotal = errorTotal + ((h(item[feature]) - item[target])**2)
return 1/(2 * len(dataset)) * errorTotal
m = 0
b = 0
# Hypothesis function
def h(x):
global m, b
return m*x + b
learningRate = 0.00000001 # Scaling should have been done better, more than that overshoots
def descend():
global m, b, learningRate
errorTotal = 0
for item in dataset:
errorTotal = errorTotal + (h(item[feature]) - item[target])
newB = b - learningRate * 1/len(dataset) * errorTotal
errorTotal = 0
for item in dataset:
errorTotal = errorTotal + (h(item[feature]) - item[target])*item[feature]
newM = m - learningRate * 1/len(dataset) * errorTotal
b = newB
m = newM
errors = [
{'error': cost(), 'iteration': 0}
]
iteration = 0
for i in range(0, 300):
descend()
iteration = iteration + 1
errors.append({'error': cost(), 'iteration': iteration})
plt.figure(1)
plt.title('Houses')
plt.plot(np.arange(0, 6000, 0.1), [h(x) for x in np.arange(0, 6000, 0.1)], 'red')
plt.scatter([item[feature] for item in dataset], [item[target] for item in dataset])
plt.xlabel('Area (sqft)')
plt.ylabel('Price ($k)')
plt.figure(2)
plt.title('Error rate')
plt.plot([error['iteration'] for error in errors], [error['error'] for error in errors], 'red')
plt.xlabel('Iteration')
plt.ylabel('Error')
plt.show()
```

This is a Linear Regression example done in Python with help of NumPy, as well as Matplotlib for plotting data. It uses Kaggle's training data as an example. This example should be directly runnable given `train.csv`

exists within the same directory. It also requires Matplotlib and NumPy, obviously.

I have implemented this after Andrew Ng's course on Coursera, and given that I am getting started it might not be the best approach. **Also note that there are very inefficient parts in code,** but these are intended to simplify code and make it easily readable, since it's only for learning purposes.

*Here's how it works step by step:*

- First it imports some Python stuff, as well as defines
`representsInt`

helper. - Then it loads the CSV file located at
`./train.csv`

to`dataset`

in the form of*list of dicts* - Then it scales the
`SalePrice`

variable. Since it's thousands of dollars, we divide by 1000 to make it $k - Two variables are defined:
`feature`

which indicates what thing we have or whatever`target`

which indicates what we look for/want to predict

- Then, a
`cost`

function is defined. The`cost`

function is Mean Squared Error, which is seemingly common for Linear Regression: - Then
`m`

and`b`

are defined for our hypothesis function. The way we are approaching this problem is by finding the the line the fits the best between the data. (see screenshot) So given that the simplest form of a line is`y = mx + b`

, all we need to tune and find good values for are`m`

and`b`

. - Then, we define our hypothesis function
`h`

, which just represents the line. - Then we implement Gradient Descent, which is basically an algorithm that minimizes functions based on their derivatives. It uses a small learning rate because our data is not well normalized, otherwise it would overshoot. We use Gradient Descent to minimize the
`cost`

: - Then
`errors`

and`iteration`

are just variables that track our hypothesis function accuracy as we apply Gradient Descent. - We do 300 steps of Gradient Descent so that it reaches a reasonable convergence.
- Plot the data.