Non-linear curve fitting in SciPy - Mini Project: Build & Apply

Non-linear Curve Fitting with SciPy

📖 Scenario: You are a scientist studying how a plant grows over time. You collected data on the plant's height at different days. You want to find a curve that best fits this growth data to understand the growth pattern.

🎯 Goal: Build a Python program that uses SciPy to fit a non-linear curve to the plant growth data and display the fitted curve parameters.

📋 What You'll Learn

Create a dictionary with days and plant heights

Define a growth model function with parameters

Use SciPy's curve_fit to find the best parameters

Print the fitted parameters

💡 Why This Matters

🌍 Real World

Scientists and engineers often collect data that follows complex patterns. Curve fitting helps find formulas that describe these patterns, making predictions easier.

💼 Career

Data scientists and analysts use curve fitting to model trends in data, which is essential in fields like biology, finance, and engineering.

1

Create the plant growth data

Create a dictionary called growth_data with these exact entries: 1: 2.5, 2: 3.6, 3: 5.1, 4: 7.4, 5: 11.2 representing days and plant heights.

SciPy

# Create the growth_data dictionary with days as keys and heights as values
# Your code here

Need a hint?

Use curly braces to create a dictionary with the exact day-height pairs.

2

Define the growth model function

Define a function called growth_model that takes t, a, and b as inputs and returns a * t ** b.

SciPy

growth_data = {1: 2.5, 2: 3.6, 3: 5.1, 4: 7.4, 5: 11.2}

# Define the growth_model function here
# Your code here

Need a hint?

The function should return the formula a * t ** b where t is time.

3

Fit the curve using SciPy

Import curve_fit from scipy.optimize. Use curve_fit with growth_model, the list of days from growth_data.keys(), and the list of heights from growth_data.values(). Store the output parameters in params.

SciPy

growth_data = {1: 2.5, 2: 3.6, 3: 5.1, 4: 7.4, 5: 11.2}

def growth_model(t, a, b):
    return a * t ** b

# Import curve_fit and fit the curve to get params
# Your code here

Need a hint?

Use list(growth_data.keys()) and list(growth_data.values()) to pass days and heights as lists.

4

Print the fitted parameters

Print the string "Fitted parameters: a = {params[0]:.2f}, b = {params[1]:.2f}" using an f-string to show the fitted values rounded to two decimals.

SciPy

from scipy.optimize import curve_fit

growth_data = {1: 2.5, 2: 3.6, 3: 5.1, 4: 7.4, 5: 11.2}

def growth_model(t, a, b):
    return a * t ** b

params, _ = curve_fit(growth_model, list(growth_data.keys()), list(growth_data.values()))

# Print the fitted parameters with two decimals
# Your code here

Need a hint?

Use print(f"Fitted parameters: a = {params[0]:.2f}, b = {params[1]:.2f}") to show the results.