You want to fit a nonlinear model y = a * exp(b * x) to data points using least_squares. Which residual function is correct?
hard📝 Application Q8 of 15
SciPy - Curve Fitting and Regression
You want to fit a nonlinear model y = a * exp(b * x) to data points using least_squares. Which residual function is correct?
Adef residuals(params):
a, b = params
return np.sum(y_data - a * np.exp(b * x_data))
Bdef residuals(params):
a, b = params
return a * np.exp(b * x_data) - y_data
Cdef residuals(params):
a, b = params
return (y_data - a * np.exp(b * x_data))**2
Ddef residuals(params):
a, b = params
return np.sum((y_data - a * np.exp(b * x_data))**2)
Step-by-Step Solution
Solution:
Step 1: Understand residuals definition
Residuals are differences between model predictions and observed data (model - data per SciPy convention).
Step 2: Check each option
A returns model - data array (residuals) [check]. B returns scalar sum(data - model), incorrect. C returns elementwise squared residuals, incorrect. D returns sum of squared residuals (scalar), incorrect.
Final Answer:
def residuals(params):
a, b = params
return a * np.exp(b * x_data) - y_data -> Option B
Quick Check:
Residuals = model - data [OK]
Quick Trick:Residuals = model prediction minus observed data [OK]
Common Mistakes:
Returning squared residuals instead of residuals
Returning sum of residuals instead of array
Confusing order of subtraction in residuals
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