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Line fits to Salar de Uyuni Data Dry Season 2012 Preliminary Results

Line fits to Salar de Uyuni Data Dry Season 2012 Preliminary Results. Location D: Plot of Full, Waxing and Waning. Data will be split into three categories: Waxing, Waning, and Full (Moon Phase < 10°). Waning Moon. First Order Polynomial (Linear). Range -10 to 11.

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Line fits to Salar de Uyuni Data Dry Season 2012 Preliminary Results

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  1. Line fits to Salar de Uyuni Data Dry Season 2012 Preliminary Results

  2. Location D: Plot of Full, Waxing and Waning Data will be split into three categories: Waxing, Waning, and Full (Moon Phase < 10°)

  3. Waning Moon

  4. First Order Polynomial (Linear) Range -10 to 11. Residuals look random. Degrees of Freedom: 40 Norm of residuals: 27.213 P(x) = -0.1659x + 77.4308

  5. Second Order Polynomial Similar to 1st Order Residuals look random. P(x) = 0.0009x² - 0.2566x + 79.1392 Degrees of Freedom: 39Norm of residuals: 27.0449

  6. Third Order Polynomial P(x) = -0.0000x³ + 0.0043x² - 0.4008x + 80.8029 Similar to 1st and 2nd as to fit. 0 value for x³ Degrees of Freedom: 38 Norm of residuals: 26.9991

  7. Waning fit comments: Not much difference between the three Orders. 2nd Order appears the best. Rerun takes out curve at end.

  8. Waxing Moon

  9. First Order Polynomial (Linear) Residuals seem to separate. Residuals between -6 to 10 One outlier at 95% confidence Degrees of Freedom: 18 Norm of residuals: 21.3404 P(x) = 0.2236x + 68.1435

  10. Second Order Polynomial Curve seems to fit better. Residuals between -7 to 7. Still one outlier at 95% conf. P(x) = 0.0095x² - 0.4611x + 78.0640 Degrees of Freedom: 17 Norm of residuals: 19.4375

  11. Third Order Polynomial Interesting curve that does seem to fit. Residuals between -7 to 4, except for one major outlier(10). P(x) = 0.0007x³ - 0.0698x² + 2.1745x + 53.3342 Degrees of Freedom: 16 Norm of residuals: 17.4951

  12. Fourth Order Polynomial Similar to 3rd Order, but left end flat. Residuals between -6 to 6; Outlier now within 95% confidence However, value 0 for x⁴ P(x) = 0.0000x⁴-0.0042x³ + 0.1791x² - 2.9487x + 88.5519 Degrees of Freedom: 16 Norm of residuals: 17.4951

  13. Waxing fit comments: 2nd Order polynomial visually looks good. One outlier at 95% confidence, with random residuals within small range around 0. 3rd Order looks interesting, but shows one major outlier in residuals 4th Order similar to 3rd Order except for left end. Residual range smaller than 2nd order. However, the coefficient for x⁴ is 0 to the fourth place.

  14. Full Moon

  15. First Order Polynomial (Linear) All data within 95% confidence Residuals spread out at > phase Range between-8 to 10 Degrees of Freedom: 9 Norm of residuals: 14.0320 P(x) = -2.8232x + 95.2369

  16. Second Order Polynomial All data within 95% confidence Residuals spread out at > phase Range smaller than 1st(-7 to 9) P(x) = -0.1101x² - 1.5609x + 92.1742 Degrees of Freedom: 8 Norm of residuals: 13.8883

  17. Third Order Polynomial All data within 95% confidence Residuals spread out at > phase Range similar to 2nd (-7 to 9) P(x) = 0.0445x³ - 0.8622x² + 2.1771x + 87.0518 Degrees of Freedom: 7 Norm of residuals: 13.7597

  18. Fourth Order Polynomial Interesting kinks to curve. Residuals look more random Range slightly smaller. P(x) = 0.0984x⁴-2.186x³ + 16.481x² - 50.848x + 137.769 Degrees of Freedom: 6 Norm of residuals: 12.5243

  19. Full Moon fit comments: 2nd Order polynomial visually looks good. Data all within 95% confidence, with random residuals within range between -7 to 9. 3rd Order not much improvement over 2nd. 4th Order is very ‘kinky’, though the fit is slightly better than 2nd. Not sure if this is what we want, though.

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