Least squares (least_squares) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the least_squares function from scipy.optimize.

SciPy

from scipy.optimize import [1]

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

Aminimize

Blinprog

Cleast_squares

Dcurve_fit

Attempts:

3 left

💡 Hint

Common Mistakes

Importing the wrong function like minimize or curve_fit.

Forgetting to import from scipy.optimize.

The least_squares function is imported from scipy.optimize to solve least squares problems.

2fill in blank

medium

Complete the code to define the residual function for least squares fitting.

SciPy

def residuals(params, x, y):
    return y - [1]

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Aparams + x

Bx * params[0] + params[1]

Cparams * x

Dparams[0] * y + params[1]

Attempts:

3 left

💡 Hint

Common Mistakes

Using params as a scalar instead of indexing.

Adding params and x directly without multiplication.

The residual function returns the difference between observed y and the model prediction x * params[0] + params[1], which is a linear model.

3fill in blank

hard

Fix the error in the least squares call to fit the model.

SciPy

result = least_squares(residuals, [1], args=(x_data, y_data))

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A[0, 0]

Bx_data

Cy_data

Dresiduals

Attempts:

3 left

💡 Hint

Common Mistakes

Passing data arrays instead of initial guess.

Passing the residual function again instead of initial guess.

The initial guess for parameters must be a list or array, here [0, 0] for slope and intercept.

4fill in blank

hard

Fill both blanks to extract the optimized parameters and print the slope.

SciPy

optimized_params = result.[1]
print('Slope:', optimized_params[2])

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Ax

By

Cparams

D[0]

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong attribute names like params or jac.

Not indexing the parameter array to get the slope.

The optimized parameters are stored in result.x. The slope is the first parameter, accessed by [0].

5fill in blank

hard

Fill all three blanks to create a dictionary of parameter names and values for slope and intercept.

SciPy

param_dict = { [1]: result.[2][0], [3]: result.x[1]}

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A'slope'

Bx

C'intercept'

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong keys or missing quotes.

Not accessing the correct indices in x.

The dictionary keys are strings: 'slope' and 'intercept'. The values come from result.x at indices 0 and 1.