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    "# Fitting Methods\n",
    "This notebook describes various methods available in the gwrefpy package for fitting observation and reference data.\n",
    "\n",
    "Currently supported fitting methods include:\n",
    "- Linear Regression\n",
    "- Nth order polynomial fitting\n",
    "- Chebyshev polynomial fitting"
   ],
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    "# Linear Regression\n",
    "The linear regression fitting method fits a straight line to the data using the least squares method. It is suitable for data that exhibits a linear relationship.\n",
    "\n",
    "The equation for a linear regression is given by:\n",
    "\n",
    "$$y = a_0 + a_1x$$\n",
    "\n",
    "where $a_0$ and $a_1$ are the coefficients."
   ],
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   "source": [
    "# Nth Order Polynomial Fitting\n",
    "The Nth order polynomial fitting method fits a polynomial of degree N to the data. This method is useful when more degrees of freedom are needed to capture the relationship between the variables.\n",
    "\n",
    "The equation for a Nth order polynomial is given by:\n",
    "\n",
    "$$y = a_0 + a_1 x + a_2 x^2 + ... + a_N x^N$$\n",
    "\n",
    "where $a_0$, $a_1$, $...$, $a_N$ are the coefficients of the polynomial."
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   "source": [
    "# Chebyshev Polynomial Fitting\n",
    "The Chebyshev polynomial fitting method uses Chebyshev polynomials to fit the data. Chebyshev polynomials are orthogonal polynomials that can provide a good approximation for functions over a specific interval.\n",
    "\n",
    "The equation for a Chebyshev polynomial of degree N is given by:\n",
    "\n",
    "$$y = a_0T_0(x) + a_1T_1(x) + a_2T_2(x) + ... + a_NT_n(x)$$\n",
    "\n",
    "where $T_N(x)$ is the Chebyshev polynomial of degree $N$ and $a_0$, $a_1$, $...$, $a_N$ are the coefficients of the polynomial. The Chebyshev polynomials are defined recursively as:\n",
    "\n",
    "$$T_0(x) = 1$$\n",
    "\n",
    "$$T_1(x) = x$$\n",
    "\n",
    "$$T_{n+1}(x) = 2xT_n(x) - T_{n-1}(x)$$"
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