Curve fitting (curve_fit) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the curve fitting function from scipy.

SciPy

from scipy.optimize import [1]

Drag options to blanks, or click blank then click option'

Aminimize

Bcurve_fit

Clinregress

Droot

Attempts:

3 left

💡 Hint

Common Mistakes

Importing the wrong function like minimize or root.

Forgetting to import from scipy.optimize.

The curve_fit function is imported from scipy.optimize to perform curve fitting.

2fill in blank

medium

Complete the code to define a linear model function for curve fitting.

SciPy

def model(x, [1], b):
    return [1] * x + b

Drag options to blanks, or click blank then click option'

Aa

Bx

Cy

Dm

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'x' as a parameter name which conflicts with input.

Using 'y' which is usually output, not parameter.

The parameter m represents the slope in the linear model m * x + b.

3fill in blank

hard

Fix the error in the code to fit the model to data using curve_fit.

SciPy

params, covariance = curve_fit(model, xdata, [1])

Drag options to blanks, or click blank then click option'

Aydata

Bparams

Cmodel

Dxdata

Attempts:

3 left

💡 Hint

Common Mistakes

Passing xdata twice.

Passing the model function instead of data.

The second argument to curve_fit after the model and xdata is the ydata (observed values).

4fill in blank

hard

Fill both blanks to create a dictionary of fitted parameters with keys 'slope' and 'intercept'.

SciPy

fitted_params = {'slope': params[1] 0, 'intercept': params[2] 1}

Drag options to blanks, or click blank then click option'

A[

B]

C(

D)

Attempts:

3 left

💡 Hint

Common Mistakes

Using parentheses instead of square brackets for indexing.

Using curly braces which are for dictionaries.

Parameters returned by curve_fit are in a list or array, so square brackets [] are used to access elements.

5fill in blank

hard

Fill all three blanks to plot the original data points and the fitted curve.

SciPy

import matplotlib.pyplot as plt

plt.scatter(xdata, ydata, label='Data')
plt.plot(xdata, model(xdata, [1], [2]), color='red', label='Fit')
plt.xlabel('[3]')
plt.ylabel('y')
plt.legend()
plt.show()

Drag options to blanks, or click blank then click option'

Aparams[0]

Bparams[1]

Cx

Dxdata

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up slope and intercept order.

Using wrong variable names for x-axis label.

Use xdata as input x-values, params[0] and params[1] as slope and intercept, and label x-axis as 'x'.

Practice

1. What is the main purpose of using curve_fit in data analysis?

easy

A. To find the best parameters that make a model fit the data points closely

B. To sort data points in ascending order

C. To calculate the average of data points

D. To remove outliers from the dataset

Solution

1. Step 1: Understand the role of curve fitting

   Curve fitting is used to find parameters of a model that best match the given data points.

2. Step 2: Identify what curve_fit does

   The curve_fit function from scipy optimizes parameters to minimize the difference between model predictions and data.

3. Final Answer:

   To find the best parameters that make a model fit the data points closely -> Option A

4. Quick Check:

   Curve fitting = best parameters for model [OK]

Hint: Remember: curve_fit finds model parameters to fit data [OK]

Common Mistakes:

• Confusing curve fitting with data sorting
• Thinking curve_fit calculates averages
• Assuming curve_fit removes outliers

2. Which of the following is the correct way to call curve_fit with a model function f, data arrays xdata and ydata?

easy

A. popt = curve_fit(f, ydata, xdata)

B. popt, pcov = curve_fit(xdata, ydata, f)

C. curve_fit(f, ydata, xdata)

D. popt, pcov = curve_fit(f, xdata, ydata)

Solution

1. Step 1: Recall the function signature of curve_fit

   The correct call is curve_fit(function, xdata, ydata), where the model function is first, then x and y data.

2. Step 2: Match the options with the correct signature

   popt, pcov = curve_fit(f, xdata, ydata) matches the correct order and unpacks both parameters and covariance matrix.

3. Final Answer:

   popt, pcov = curve_fit(f, xdata, ydata) -> Option D

4. Quick Check:

   curve_fit(function, xdata, ydata) [OK]

Hint: Remember order: function, xdata, ydata in curve_fit [OK]

Common Mistakes:

• Swapping xdata and ydata
• Not unpacking both outputs
• Passing arguments in wrong order

3. Given the code:

import numpy as np
from scipy.optimize import curve_fit

def model(x, a, b):
    return a * x + b

xdata = np.array([1, 2, 3, 4, 5])
ydata = np.array([2.1, 4.1, 6.0, 8.1, 10.2])

popt, pcov = curve_fit(model, xdata, ydata)
print(np.round(popt, 2))

What will be printed?

medium

A. [2.00 0.00]

B. [2.02 0.04]

C. [1.00 2.00]

D. [0.06 2.04]

Solution

1. Step 1: Understand the model and data

   The model is linear: y = a*x + b. The data roughly follows y = 2*x + 0.

2. Step 2: Use curve_fit to find parameters

   Running curve_fit finds parameters close to a=2.02 and b=0.04, fitting the data closely.

3. Final Answer:

   [2.02 0.04] -> Option B

4. Quick Check:

   Fitted slope ~2.02, intercept ~0.04 [OK]

Hint: Check model form and data trend to guess parameters [OK]

Common Mistakes:

• Confusing parameter order
• Ignoring rounding
• Assuming exact integers

4. Consider this code snippet:

import numpy as np
from scipy.optimize import curve_fit

def model(x, a, b):
    return a * x + b

xdata = np.array([1, 2, 3])
ydata = np.array([2, 4, 6])

popt, pcov = curve_fit(model, ydata, xdata)
print(popt)

What is the main issue here?

medium

A. The model function is incorrect

B. The data arrays have different lengths

C. xdata and ydata are swapped in curve_fit call

D. curve_fit cannot handle linear models

Solution

1. Step 1: Check the order of arguments in curve_fit

   The correct order is curve_fit(model, xdata, ydata). Here, ydata and xdata are swapped.

2. Step 2: Understand the impact of swapping

   Swapping causes the model to fit x as a function of y, which is not intended and leads to wrong parameters.

3. Final Answer:

   xdata and ydata are swapped in curve_fit call -> Option C

4. Quick Check:

   Order is model, xdata, ydata [OK]

Hint: Always put xdata before ydata in curve_fit [OK]

Common Mistakes:

• Swapping xdata and ydata
• Assuming model function is wrong
• Ignoring argument order importance

5. You have noisy data from a quadratic process: y = a*x**2 + b*x + c. You want to fit this model using curve_fit. Which of the following code snippets correctly defines the model and fits the data xdata, ydata?

hard

A. def model(x, a, b, c):
return a * x**2 + b * x + c
popt, pcov = curve_fit(model, xdata, ydata)

B. def model(a, b, c, x):
return a * x**2 + b * x + c
popt, pcov = curve_fit(model, xdata, ydata)

C. def model(x, a, b):
return a * x**2 + b * x
popt, pcov = curve_fit(model, xdata, ydata)

D. def model(x, a, b, c):
return a * x + b * x**2 + c
popt, pcov = curve_fit(model, ydata, xdata)

Solution

1. Step 1: Define the model function correctly

   The model must have x as the first argument, followed by parameters a, b, c. The formula is a*x**2 + b*x + c.

2. Step 2: Call curve_fit with correct argument order

   Use curve_fit(model, xdata, ydata) to fit the model to data.

3. Final Answer:

   def model(x, a, b, c): return a * x**2 + b * x + c popt, pcov = curve_fit(model, xdata, ydata) -> Option A

4. Quick Check:

   Model args: x first, then parameters; curve_fit(model, xdata, ydata) [OK]

Hint: Model function: x first, parameters next; call curve_fit accordingly [OK]

Common Mistakes:

• Putting parameters before x in model
• Missing one parameter in model
• Swapping xdata and ydata in curve_fit