Least squares optimization in SciPy - Mini Project: Build & Apply

Least squares optimization

📖 Scenario: You are working as a data scientist helping a small business understand the relationship between advertising spending and sales. You have collected data on advertising budgets and sales figures. Your goal is to find the best straight line that fits this data using least squares optimization.

🎯 Goal: Build a simple least squares optimization model using scipy.optimize.least_squares to find the best line parameters (slope and intercept) that fit the sales data.

📋 What You'll Learn

Create arrays for advertising budgets and sales data

Define a residual function for the least squares method

Use scipy.optimize.least_squares to find the best slope and intercept

Print the optimized slope and intercept values

💡 Why This Matters

🌍 Real World

Least squares optimization is used in many fields like economics, engineering, and science to find the best fit model for data.

💼 Career

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

1

Create the data arrays

Create two numpy arrays called advertising and sales with these exact values: advertising = [5, 10, 15, 20, 25] and sales = [7, 12, 14, 22, 27].

SciPy

import numpy as np
# Create the advertising and sales arrays
# Your code here

Need a hint?

Use np.array([...]) to create numpy arrays with the given values.

2

Define the residual function

Define a function called residuals that takes params as input. Inside, unpack params into slope and intercept. Return the difference between the predicted sales (slope * advertising + intercept) and the actual sales.

SciPy

import numpy as np
advertising = np.array([5, 10, 15, 20, 25])
sales = np.array([7, 12, 14, 22, 27])

# Define the residuals function
# Your code here

Need a hint?

The residuals function calculates how far off the predicted sales are from the actual sales for given slope and intercept.

3

Run least squares optimization

Import least_squares from scipy.optimize. Use least_squares with the residuals function and an initial guess [1, 0] for slope and intercept. Store the result in a variable called result.

SciPy

import numpy as np
advertising = np.array([5, 10, 15, 20, 25])
sales = np.array([7, 12, 14, 22, 27])

def residuals(params):
    slope, intercept = params
    return slope * advertising + intercept - sales

# Import least_squares and run optimization
# Your code here

Need a hint?

Use least_squares(residuals, [1, 0]) to start with slope=1 and intercept=0.

4

Print the optimized parameters

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

SciPy

import numpy as np
advertising = np.array([5, 10, 15, 20, 25])
sales = np.array([7, 12, 14, 22, 27])

def residuals(params):
    slope, intercept = params
    return slope * advertising + intercept - sales

from scipy.optimize import least_squares
result = least_squares(residuals, [1, 0])

# Print the optimized slope and intercept
# Your code here

Need a hint?

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