UnivariateSpline in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Spline Evaluation

What is the output of the following code snippet that fits a UnivariateSpline and evaluates it at x=2.5?

SciPy

import numpy as np
from scipy.interpolate import UnivariateSpline

x = np.array([1, 2, 3, 4, 5])
y = np.array([1, 4, 9, 16, 25])
spline = UnivariateSpline(x, y, s=0)
result = spline(2.5)
print(round(result, 2))

A 9.0

B 7.0

C 6.25

D 8.5

💡 Hint

Think about the shape of y = x^2 and how spline fits exactly with s=0.

The spline fits the points exactly because smoothing factor s=0. At x=2.5, y = 2.5^2 = 6.25, so the spline returns 6.25.

❓ data_output

intermediate

Number of Knots in Spline

After fitting a UnivariateSpline with smoothing factor s=1 on the data below, how many knots does the spline have?

SciPy

import numpy as np
from scipy.interpolate import UnivariateSpline

x = np.linspace(0, 10, 11)
y = np.sin(x)
spline = UnivariateSpline(x, y, s=1)
knots_count = len(spline.get_knots())
print(knots_count)

A 7

B 11

C 5

D 9

💡 Hint

Smoothing reduces the number of knots compared to the number of data points.

With smoothing s=1, the spline reduces knots from 11 data points to fewer knots, here 9 knots are returned.

🔧 Debug

advanced

Error Raised by Incorrect Input

What error does the following code raise when trying to fit a UnivariateSpline?

SciPy

import numpy as np
from scipy.interpolate import UnivariateSpline

x = np.array([1, 2, 2, 4, 5])
y = np.array([1, 4, 9, 16, 25])
spline = UnivariateSpline(x, y, s=0)

A ValueError: x must be strictly increasing

B TypeError: unsupported operand type(s) for -: 'list' and 'int'

C IndexError: index out of range

D No error, code runs successfully

💡 Hint

Check the x array for duplicates or ordering.

UnivariateSpline requires x values to be strictly increasing. Duplicate 2's cause ValueError.

🚀 Application

advanced

Choosing Smoothing Factor for Noisy Data

You have noisy data points and want to fit a smooth curve using UnivariateSpline. Which smoothing factor s is most appropriate to reduce noise but keep the trend?

A s = 0 (no smoothing, exact fit)

B s = large positive value (more smoothing)

C s = negative value

D s = None (default)

💡 Hint

More smoothing means less sensitivity to noise.

A larger positive s smooths the spline, reducing noise effects while preserving the overall trend.

🧠 Conceptual

expert

Effect of Spline Degree on Fit

How does increasing the degree k of a UnivariateSpline from 1 to 3 affect the fitted curve?

A The spline becomes smoother and can model curvature better

B The spline becomes less smooth and more linear

C The spline ignores data points and fits a constant line

D The spline raises an error because degree must be 1

💡 Hint

Higher degree splines can model curves better than linear splines.

Increasing degree k allows the spline to fit curves with more flexibility and smoothness.