Which of the following correctly defines a custom model function compatible with scipy.optimize.curve_fit to fit a cubic polynomial y = a*x**3 + b*x**2 + c*x + d?
easy📝 Conceptual Q3 of 15
SciPy - Curve Fitting and Regression
Which of the following correctly defines a custom model function compatible with scipy.optimize.curve_fit to fit a cubic polynomial y = a*x**3 + b*x**2 + c*x + d?
Adef cubic_model(x, a, b, c, d):
return a * x**3 + b * x + c * x**2 + d
Bdef cubic_model(a, b, c, d, x):
return a * x**3 + b * x**2 + c * x + d
Cdef cubic_model(x, a, b, c):
return a * x**3 + b * x**2 + c * x + d
Ddef cubic_model(x, a, b, c, d):
return a * x**3 + b * x**2 + c * x + d
Step-by-Step Solution
Solution:
Step 1: Define function with x as first argument
The model function must have the independent variable x as the first parameter.
Step 2: Include all parameters in order
All coefficients a, b, c, d must be parameters after x.
Step 3: Correct polynomial expression
The function should return a*x**3 + b*x**2 + c*x + d exactly.
Final Answer:
def cubic_model(x, a, b, c, d):
return a * x**3 + b * x**2 + c * x + d correctly defines the model function.
Quick Check:
Function signature and return expression match [OK]
Quick Trick:Model function: x first, then parameters [OK]
Common Mistakes:
Placing parameters before x
Missing one or more parameters
Incorrect polynomial terms order
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