# curve fitting examples

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## curve fitting examples

 Hello everyone, I retrieve some data, which can have missing data points even in the beginning or at the end. So what I needed was both; interpolation as well as extrapolation, to fill these positions. Typically the deviation over the data is not that huge and a straight fitting works well under this circumstance. Otherwise on more fluctuating/arbitrary data I got no satisfying results with any of the available fitting functions (see example makro below). Maybe my expectations are wrong about this and I thought that there is a way to adjusted methods in how close a resulting fitting would be applied. So I used median/mean as prefilter-methods. What wonders me is that sometimes a certain method works very well. In my case Rodbard, Error or a Gaussian. But sometimes, like in the given example, it makes no sense to use these at all. Is this typical or is my data strange :) Regards, Rainer // START (makro) ############################################# // Curve Fitting Demo // // This macro demonstates how to use the Fit.* functions, // which were added to the macro language in v1.41k. // modified to see some larger data sets x = newArray(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339); y = newArray(96, 97, 98, 101, 101, 102, 101, 101, 101, 101, 101, 101, 100, 100, 101, 101, 102, 101, 100, 100, 101, 100, 99, 99, 100, 101, 100, 100, 101, 101, 100, 99, 99, 99, 99, 99, 99, 98, 99, 99, 98, 97, 96, 96, 96, 96, 95, 94, 95, 95, 94, 94, 93, 90, 89, 89, 88, 87, 87, 87, 87, 84, 85, 84, 85, 84, 83, 81, 81, 81, 80, 80, 78, 77, 77, 77, 76, 75, 75, 75, 75, 74, 73, 73, 73, 73, 72, 71, 71, 71, 70, 69, 68, 68, 68, 67, 66, 66, 65, 66, 65, 66, 64, 64, 64, 64, 64, 65, 65, 66, 66, 65, 65, 65, 65, 66, 66, 66, 67, 68, 68, 68, 68, 69, 69, 70, 69, 69, 69, 70, 70, 71, 70, 72, 72, 72, 71, 71, 72, 73, 73, 73, 73, 75, 75, 75, 74, 75, 75, 76, 76, 77, 76, 76, 77, 78, 77, 77, 77, 78, 79, 80, 79, 79, 80, 81, 80, 80, 81, 81, 81, 80, 81, 81, 82, 82, 82, 81, 82, 83, 83, 83, 82, 83, 83, 83, 82, 84, 84, 84, 84, 84, 83, 83, 84, 84, 83, 84, 84, 84, 83, 83, 83, 83, 85, 85, 84, 83, 84, 84, 84, 83, 83, 84, 84, 85, 84, 83, 83, 84, 83, 83, 83, 83, 84, 83, 83, 84, 84, 84, 84, 84, 83, 84, 84, 84, 83, 83, 83, 84, 84, 83, 83, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 85, 84, 85, 84, 83, 83, 84, 84, 84, 84, 85, 85, 84, 83, 84, 84, 83, 84, 83, 84, 85, 84, 84, 84, 84, 84, 85, 84, 83, 83, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 85, 84, 84, 84, 83, 83, 84, 84, 83, 83, 84, 84, 84, 83, 83, 84, 84, 84, 84, 83, 83, 84, 84, 83, 82, 83, 83, 83, 83, 83, 83, 84, 84, 83, 83, 83, 84, 84, 83, 83, 83, 83); doAllCurveFittings("raw", x, y); //pretty dense x-range x = newArray(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339); y = newArray(100.8147, 100.7783, 100.7480, 100.6839, 100.6290, 100.6147, 100.6335, 100.6794, 100.6647, 100.6252, 100.5897, 100.5647, 100.5397, 100.4647, 100.3897, 100.3647, 100.3647, 100.3147, 100.2897, 100.2897, 100.3147, 100.2897, 100.2147, 100.1647, 100.0897, 100.0147, 99.9147, 99.7897, 99.6647, 99.5897, 99.5397, 99.4147, 99.2647, 99.1147, 98.9397, 98.7147, 98.4397, 98.1897, 97.8897, 97.5897, 97.2647, 96.9647, 96.7147, 96.3897, 96.0730, 95.7147, 95.3397, 94.9480, 94.5897, 94.1897, 93.7147, 93.2397, 92.7897, 92.3397, 91.8897, 91.4147, 90.9647, 90.4397, 89.9647, 89.4397, 88.9647, 88.4647, 87.9147, 87.3647, 86.8064, 86.2397, 85.6647, 85.0814, 84.4397, 83.7647, 83.1647, 82.5897, 81.9897, 81.3897, 80.8147, 80.2397, 79.6647, 79.1147, 78.5147, 77.9397, 77.3147, 76.7397, 76.1897, 75.6397, 75.1147, 74.6147, 74.1147, 73.5647, 73.0397, 72.5647, 72.0647, 71.5397, 71.0147, 70.5397, 70.0147, 69.5397, 69.0397, 68.6397, 68.1647, 67.6897, 67.2397, 66.7897, 66.3897, 66.0897, 65.7897, 65.5397, 65.3147, 65.1397, 64.9897, 64.8647, 64.7397, 64.6897, 64.7147, 64.7147, 64.7897, 64.9147, 65.0397, 65.1397, 65.3647, 65.6147, 65.8647, 66.1647, 66.3897, 66.6147, 66.8397, 67.0647, 67.3147, 67.6147, 67.9147, 68.2647, 68.6147, 68.9147, 69.1647, 69.4397, 69.7147, 69.9647, 70.2397, 70.5147, 70.7647, 71.0897, 71.4147, 71.6897, 71.9897, 72.3147, 72.6147, 72.9147, 73.1897, 73.4647, 73.7147, 73.9147, 74.1647, 74.4397, 74.7147, 74.9897, 75.2397, 75.4647, 75.7397, 76.0647, 76.3397, 76.5397, 76.7897, 77.0647, 77.3397, 77.5397, 77.8147, 78.0647, 78.3147, 78.4897, 78.7397, 78.9897, 79.2397, 79.4647, 79.7147, 79.9397, 80.1897, 80.4647, 80.6897, 80.8397, 81.0147, 81.2147, 81.3647, 81.4897, 81.6147, 81.8397, 82.0147, 82.1647, 82.3147, 82.5147, 82.6397, 82.7647, 82.8647, 82.9647, 83.0647, 83.2147, 83.3147, 83.3647, 83.3647, 83.4147, 83.4897, 83.5147, 83.6147, 83.7397, 83.8397, 83.8147, 83.8147, 83.8147, 83.8397, 83.7897, 83.8147, 83.8397, 83.8397, 83.8897, 83.9147, 83.8647, 83.8397, 83.8397, 83.8397, 83.8397, 83.8397, 83.8397, 83.7897, 83.6897, 83.6147, 83.6397, 83.6397, 83.6397, 83.6147, 83.6647, 83.6397, 83.6397, 83.6647, 83.6147, 83.5647, 83.5647, 83.5397, 83.5397, 83.5897, 83.5647, 83.5647, 83.5897, 83.6147, 83.6647, 83.7147, 83.7147, 83.7147, 83.7397, 83.7647, 83.7897, 83.8397, 83.8897, 83.8897, 83.9397, 83.9897, 84.0147, 84.0397, 84.0647, 84.0897, 84.1647, 84.2147, 84.2647, 84.2897, 84.2897, 84.2897, 84.2897, 84.2897, 84.2397, 84.2397, 84.1897, 84.2147, 84.2147, 84.2397, 84.2397, 84.2897, 84.3397, 84.3897, 84.4397, 84.4397, 84.3897, 84.3647, 84.3397, 84.3147, 84.3397, 84.3647, 84.3897, 84.4147, 84.4647, 84.4897, 84.5397, 84.5397, 84.5397, 84.5397, 84.5147, 84.4897, 84.4397, 84.4147, 84.3647, 84.3647, 84.3897, 84.3647, 84.3647, 84.3397, 84.3147, 84.2647, 84.2147, 84.2147, 84.2147, 84.1897, 84.1647, 84.1147, 84.0647, 84.0397, 84.0397, 83.9897, 83.9647, 83.9397, 83.9147, 83.8647, 83.8397, 83.8397, 83.7897, 83.8147, 83.8147, 83.8147, 83.8147, 83.7647, 83.7147, 83.6647, 83.6397, 83.6647, 83.6647, 83.6647, 83.6252, 83.6369, 83.6794, 83.6960, 83.6814, 83.7004, 83.7224, 83.7480, 83.7783); doAllCurveFittings("pre-filtered", x, y); //full x-range function doAllCurveFittings(stackTitle, xpoints, ypoints) {         // Do a straight line fit         Fit.doFit("Straight Line", xpoints, ypoints);         //print("a="+d2s(Fit.p(0),6)+", b="+d2s(Fit.p(1),6));                 // Do all possible fits, plot them and add the plots to a stack         setBatchMode(true);         for (i=0; i
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