Linear regression with np.polyfit() in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of np.polyfit() coefficients

What is the output of the following code?

import numpy as np
x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 4, 6, 8, 10])
coeffs = np.polyfit(x, y, 1)
print(coeffs)

NumPy

import numpy as np
x = np.array([1, 2, 3, 4, 5])
y = np.array([2, 4, 6, 8, 10])
coeffs = np.polyfit(x, y, 1)
print(coeffs)

A [2.0, 1.0]

B [0.0, 2.0]

C [2.0, 0.0]

D [1.0, 2.0]

💡 Hint

Remember np.polyfit returns coefficients starting with the highest degree term.

np.polyfit(x, y, 1) fits a line y = mx + b. The output is [m, b]. Here, slope m=2.0 and intercept b=0.0.

❓ data_output

intermediate

Number of points predicted by polyfit model

Given the code below, how many predicted y-values are generated?

import numpy as np
x = np.array([0, 1, 2, 3])
y = np.array([1, 3, 5, 7])
coeffs = np.polyfit(x, y, 1)
predicted_y = np.polyval(coeffs, x)
print(len(predicted_y))

NumPy

import numpy as np
x = np.array([0, 1, 2, 3])
y = np.array([1, 3, 5, 7])
coeffs = np.polyfit(x, y, 1)
predicted_y = np.polyval(coeffs, x)
print(len(predicted_y))

A 4

B 1

C 5

D 3

💡 Hint

The predicted values are calculated for each x input point.

np.polyval evaluates the polynomial at each x value, so the output length matches input x length.

🔧 Debug

advanced

Error raised by incorrect np.polyfit usage

What error does this code raise?

import numpy as np
x = np.array([1, 2, 3])
y = np.array([2, 4])
coeffs = np.polyfit(x, y, 1)

NumPy

import numpy as np
x = np.array([1, 2, 3])
y = np.array([2, 4])
coeffs = np.polyfit(x, y, 1)

A ValueError: x and y must have same length

B TypeError: unsupported operand type(s)

C IndexError: index out of range

D No error, runs successfully

💡 Hint

Check if x and y arrays have the same size.

np.polyfit requires x and y arrays to be the same length. Here, x has 3 elements, y has 2, so it raises ValueError.

🧠 Conceptual

advanced

Interpretation of np.polyfit output array

If np.polyfit(x, y, 2) returns [3, -2, 5], what is the polynomial equation it represents?

A 5x^2 - 2x + 3

B 3x^2 - 2x + 5

C 3x + (-2)x^2 + 5

D 5x + (-2)x^2 + 3

💡 Hint

np.polyfit returns coefficients from highest degree to constant term.

The array [3, -2, 5] means 3*x^2 - 2*x + 5.

🚀 Application

expert

Predicting new values using np.polyfit and np.polyval

You fit a line to data x=[1,2,3,4], y=[2,3,5,7] using np.polyfit with degree 1. What is the predicted y value for x=5?

import numpy as np
x = np.array([1, 2, 3, 4])
y = np.array([2, 3, 5, 7])
coeffs = np.polyfit(x, y, 1)
predicted_y = np.polyval(coeffs, 5)
print(round(predicted_y, 2))

NumPy

import numpy as np
x = np.array([1, 2, 3, 4])
y = np.array([2, 3, 5, 7])
coeffs = np.polyfit(x, y, 1)
predicted_y = np.polyval(coeffs, 5)
print(round(predicted_y, 2))

A 9.5

B 10.0

C 7.5

D 8.5

💡 Hint

Calculate slope and intercept from polyfit, then evaluate at x=5.

The fitted line is approximately y = 1.7x + 0.1, so at x=5, y ≈ 8.5.