Least squares (least_squares) in SciPy - Mini Project: Build & Apply

Fitting a Line Using Least Squares

📖 Scenario: You have collected some data points about the hours studied and the scores obtained by students in a test. You want to find the best straight line that fits this data to predict scores based on hours studied.

🎯 Goal: Build a simple linear model using the least_squares function from scipy.optimize to find the best fit line for the data points.

📋 What You'll Learn

Create arrays for hours studied and scores obtained

Define a function to calculate residuals between predicted and actual scores

Use least_squares to find the best fit parameters

Print the best fit slope and intercept

💡 Why This Matters

🌍 Real World

Least squares fitting is used in many fields like economics, biology, and engineering to find trends and make predictions from data.

💼 Career

Data scientists and analysts use least squares methods to build predictive models and understand relationships between variables.

1

Create the data arrays

Create two numpy arrays called hours and scores with these exact values: hours = [1, 2, 3, 4, 5] and scores = [1.5, 3.7, 3.2, 5.5, 6.1].

SciPy

import numpy as np
# Create numpy arrays hours and scores with given values
# Your code here

Need a hint?

Use np.array to create arrays from the lists.

2

Define the residuals function

Define a function called residuals that takes a parameter array params and returns the difference between predicted scores and actual scores. Use the formula predicted = params[0] * hours + params[1] inside the function.

SciPy

import numpy as np
hours = np.array([1, 2, 3, 4, 5])
scores = np.array([1.5, 3.7, 3.2, 5.5, 6.1])
# Define residuals function here
# Your code here

Need a hint?

The function should return the difference between predicted and actual scores.

3

Use least_squares to find best fit

Import least_squares from scipy.optimize. Then call least_squares with the residuals function and an initial guess [1, 0]. Save the result in a variable called result.

SciPy

import numpy as np
hours = np.array([1, 2, 3, 4, 5])
scores = np.array([1.5, 3.7, 3.2, 5.5, 6.1])
def residuals(params):
    predicted = params[0] * hours + params[1]
    return predicted - scores
# Import least_squares and call it with residuals and initial guess [1, 0]
# Your code here

Need a hint?

Use from scipy.optimize import least_squares and call least_squares(residuals, [1, 0]).

4

Print the best fit parameters

Print the slope and intercept from result.x using print(f"Slope: {result.x[0]:.2f}, Intercept: {result.x[1]:.2f}").

SciPy

import numpy as np
from scipy.optimize import least_squares

hours = np.array([1, 2, 3, 4, 5])
scores = np.array([1.5, 3.7, 3.2, 5.5, 6.1])

def residuals(params):
    predicted = params[0] * hours + params[1]
    return predicted - scores

result = least_squares(residuals, [1, 0])
# Print slope and intercept from result.x
# Your code here

Need a hint?

Use print(f"Slope: {result.x[0]:.2f}, Intercept: {result.x[1]:.2f}") to show the results rounded to two decimals.