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What will be the shape of the covariance matrix returned by curve_fit when fitting a model with 3 parameters?

medium📝 Conceptual Q5 of 15
SciPy - Curve Fitting and Regression
What will be the shape of the covariance matrix returned by curve_fit when fitting a model with 3 parameters?
A(1, 1)
B(1, 3)
C(3, 3)
D(3, 1)
Step-by-Step Solution
Solution:
  1. Step 1: Recall covariance matrix size

    The covariance matrix size matches the number of parameters squared.
  2. Step 2: For 3 parameters, matrix is 3x3

    Each parameter has variance and covariance with others, so shape is (3, 3).
  3. Final Answer:

    (3, 3) -> Option C
  4. Quick Check:

    Covariance matrix shape = (num_params, num_params) [OK]
Quick Trick: Covariance matrix is square with size = number of parameters [OK]
Common Mistakes:
  • Confusing shape with parameter vector shape
  • Expecting 1D array instead of 2D matrix
  • Assuming covariance matrix is scalar

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