Python Coding challenge - Day 424| What is the output of the following Python Code?

 

Step-by-Step Breakdown

1. Import Required Libraries

import statsmodels.api as sm  

import numpy as np  

statsmodels.api is a Python library for statistical modeling, including Ordinary Least Squares (OLS) regression.

numpy is used for handling arrays.

2. Define Input Data

x = np.array([1, 2, 3, 4, 5])  

y = np.array([3, 6, 9, 12, 15])  

x represents the independent variable (predictor).

y represents the dependent variable (response).

The relationship follows a perfect linear pattern:

y=3x

This means the data is already perfectly aligned with a straight line.

3. Add Constant Term for Intercept

X = sm.add_constant(x)

sm.add_constant(x) adds a column of ones to x, which allows the regression model to estimate the intercept in the equation:

y=mx+c

After this step, X looks like:

[[1, 1],

 [1, 2],

 [1, 3],

 [1, 4],

 [1, 5]]

where:

The first column (all 1s) represents the intercept.

The second column is the original x values.

4. Fit the OLS Model

model = sm.OLS(y, X).fit()

sm.OLS(y, X).fit() performs Ordinary Least Squares (OLS) regression, which finds the best-fitting line by minimizing the sum of squared residuals.

5. Print the Slope (Coefficient)

print(model.params[1])

.params gives the estimated coefficients [intercept, slope].

model.params[1] extracts the slope (coefficient of x).

Final Output

3