[Solved] Analyze the output of this code:import numpy as np from scipy.optimize import curve_fit def cubic(x, a, b, c, d): return a*x**3 + b*x**2 + c*x + d x_points = np.array([0, 1, 2, 3]) y_points = np.... | SciPy

SciPy - Curve Fitting and Regression

Analyze the output of this code:

import numpy as np
from scipy.optimize import curve_fit

def cubic(x, a, b, c, d):
    return a*x**3 + b*x**2 + c*x + d

x_points = np.array([0, 1, 2, 3])
y_points = np.array([1, 6, 17, 34])

params, _ = curve_fit(cubic, x_points, y_points)
print(np.round(params, 2))

What will be printed?

A[1.0, 0.5, 1.5, 1.0]

B[1.0, 1.0, 2.0, 0.0]

C[0.5, 1.5, 2.0, 1.0]

D[1.0, 0.0, 2.0, 1.0]

Step-by-Step Solution

Solution:

Step 1: Understand the cubic model
The function is y = a*x^3 + b*x^2 + c*x + d.
Step 2: Check given data points
At x=0, y=1 implies d=1. The other points fit y = x^3 + 2x + 1.
Step 3: Use curve_fit output
Fitting will find parameters close to a=1, b=0, c=2, d=1.
Final Answer:
[1.0, 0.0, 2.0, 1.0] -> Option D
Quick Check:
Parameters match the polynomial generating y [OK]

Quick Trick: Coefficients reflect polynomial generating data [OK]

Common Mistakes:

Misinterpreting parameter order
Ignoring constant term from x=0 data
Assuming non-zero quadratic term without evidence

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Analyze the output of this code:

Step 1: Understand the cubic model

Step 2: Check given data points

Step 3: Use curve_fit output

Final Answer:

Quick Check:

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