Power Function Fitting with MATLAB Code

Power function fitting in MATLAB is a common curve fitting operation typically used to analyze data exhibiting power-law relationships. The general form of a power function is y = a * x^b, where a and b are parameters to be estimated through fitting.

### Basic Approach Defining the power function model: Typically implemented using anonymous functions (@(b,x) b(1)*x.^b(2)) or custom function files to define the power function form for subsequent calls. Data preparation: Ensure input data x and y are matching vectors/arrays, removing potential NaN values or outliers using functions like isnan() or rmoutliers(). Parameter fitting: Employ optimization functions like nlinfit, lsqcurvefit, or fit for nonlinear least squares fitting, utilizing algorithms like Levenberg-Marquardt to find optimal a and b parameters. Fit evaluation: Calculate metrics like R² (coefficient of determination) and RMSE (root mean square error) using corrcoef() and custom calculations to assess fitting quality.

### Extended Optimization Logarithmic transformation method: For large data ranges, apply logarithmic transformation (log(y) = log(a) + b*log(x)) to convert to linear fitting, using polyfit for polynomial fitting then reverse-calculating parameters through exponentiation. Weighted fitting: For data with heteroscedasticity, implement weighted least squares using weights in lsqcurvefit or fitoptions to improve fitting precision. Multi-parameter fitting: For more complex models like y = a * x^b + c, simply extend the function definition by adding parameters and adjusting the optimization function call accordingly.

By appropriately selecting fitting methods and evaluation metrics, MATLAB enables efficient power function fitting implementation, applicable to data analysis across various fields including engineering, biology, and finance.