Summary  
Demonstrates how to compute parameters of a simple linear regression model using NumPy’s polyfit, visualize the fitted line, and generate predictions from the resulting model.

General domain of usage  
Predictive modeling

You already know what simple linear regression is and how to find the line that fits the data best. You will now go through all the steps of building a linear regression for a real dataset.

## Loading Data
We have a file, `simple_height_data.csv`, with the data from our examples. We'll load the file and take a look at it:

import pandas as pd

file_link = 'https://codefinity-content-media.s3.eu-west-1.amazonaws.com/b22d1166-efda-45e8-979e-6c3ecfc566fc/simple_height_data.csv'
df = pd.read_csv(file_link)	# Read the file

print(df.head())	# Print the first 5 instances from a dataset

So the dataset has two columns: the first is `'Father'`, which is the **input feature**, and the second is `'Height'`, which is our **target variable**.

We'll assign our target values to the `y` variable and feature values to `X` and build a scatterplot.

import matplotlib.pyplot as plt

X = df['Father']	# Assign the feature
y = df['Height']	# Assign the target
plt.scatter(X,y)	# Build scatterplot
plt.show()

## Finding Parameters
Now, NumPy has a nice function to find the parameters of linear regression.

Linear Regression is a Polynomial Regression of degree 1 (we will talk about Polynomial Regression in later sections). That's why we need to put `deg=1` to get the parameters for the linear regression.  
Here is an example:

import numpy as np

beta_1, beta_0 = np.polyfit(X, y, 1)	# Get the parameters
print('beta_0 is', beta_0)
print('beta_1 is', beta_1)

If you are unfamiliar with the syntax `beta_1, beta_0 = np.polyfit(X,y,1)`, that is called unpacking. If you have an iterator (e.g., list or NumPy array or pandas series) that has two items writing 
```python
a, b = my_iterator
```
is the same as
```python
a = my_iterator[0]
b = my_iterator[1]
```
And since the return of a `polyfit()` function is a NumPy array with two values, we are allowed to do that.

Note

## Making the Predictions
Now we can plot the line and predict new variables using the parameters.

plt.scatter(X,y)	# Build a scatter plot
plt.plot(X, beta_0 + beta_1 * X, color='red')	# Plot the line
plt.show()

Now that we have the parameters, we can use the linear regression equation to predict new values.

X_new = np.array([65, 70, 75])	# Feature values of new instances
y_pred = beta_0 + beta_1 * X_new	# Predict the target
print('Predicted y: ', y_pred)

So it is pretty easy to get the parameters of the linear regression. But some libraries can also give you some extra information.

You can find the parameters of Simple Linear Regression using the NumPy's function:

Explores regression techniques for modeling and predicting continuous outcomes using Python. Builds on linear regression foundations to analyze relationships between variables, interpret model coefficients, and evaluate predictive performance on real-world datasets.


Building Linear Regression Using NumPy

Loading Data

Finding Parameters

Making the Predictions