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"This notebook describes various methods available in the gwrefpy package for fitting observation and reference data.\n",
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"\n",
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"Currently supported fitting methods include:\n",
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"- Linear Regression\n",
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"- Nth order polynomial fitting\n",
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"- Chebyshev polynomial fitting"
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],
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"id": "c50ea0e738fe2d39"
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "initial_id",
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": ""
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},
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{
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"metadata": {},
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"cell_type": "markdown",
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"source": [
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"# Linear Regression\n",
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"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",
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"\n",
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"The equation for a linear regression is given by:\n",
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"\n",
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"$$y = a_0 + a_1x$$\n",
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"\n",
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"where $a_0$ and $a_1$ are the coefficients."
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],
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"id": "154554bb0b406c88"
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},
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{
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"metadata": {},
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"cell_type": "markdown",
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"source": [
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"# Nth Order Polynomial Fitting\n",
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"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",
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"\n",
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"The equation for a Nth order polynomial is given by:\n",
"where $a_0$, $a_1$, $...$, $a_N$ are the coefficients of the polynomial."
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],
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"id": "a226ea44aebc824f"
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},
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{
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"metadata": {},
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"cell_type": "markdown",
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"source": "",
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"id": "dbe8afaba89fa1c5"
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},
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{
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"metadata": {},
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"cell_type": "markdown",
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"source": [
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"# Chebyshev Polynomial Fitting\n",
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"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",
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"\n",
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"The equation for a Chebyshev polynomial of degree N is given by:\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",
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