Line fits to Salar de Uyuni DataDry 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)

P(x) = -0.1659x + 77.4308Degrees of Freedom: 40Norm of residuals: 27.213

Range -10 to 11. Residuals look random.

Second Order Polynomial

P(x) = 0.0009x² - 0.2566x + 79.1392

Degrees of Freedom: 39 Norm of residuals: 27.0449

Similar to 1st OrderResiduals look random.

Third Order Polynomial

P(x) = -0.0000x³ + 0.0043x² - 0.4008x + 80.8029

Degrees of Freedom: 38 Norm of residuals: 26.9991

Similar to 1st and 2nd as to fit. 0 value for x³

Waning fit comments:

Not much difference between the three Orders.

2nd Order appears the best.

Rerun takes out curve at end.

Waxing Moon

First Order Polynomial (Linear)

P(x) = 0.2236x + 68.1435 Degrees of Freedom: 18Norm of residuals: 21.3404

Residuals seem to separate.Residuals between -6 to 10One outlier at 95% confidence

Second Order Polynomial

P(x) = 0.0095x² - 0.4611x + 78.0640

Degrees of Freedom: 17 Norm of residuals: 19.4375

Curve seems to fit better. Residuals between -7 to 7.Still one outlier at 95% conf.

Third Order Polynomial

P(x) = 0.0007x³ - 0.0698x² + 2.1745x + 53.3342

Degrees of Freedom: 16 Norm of residuals: 17.4951

Interesting curve that does seem to fit. Residuals between -7 to 4, except for one major outlier(10).

Fourth Order Polynomial

P(x) = 0.0000x⁴-0.0042x³ + 0.1791x² - 2.9487x + 88.5519

Degrees of Freedom: 16 Norm of residuals: 17.4951

Similar to 3rd Order, but left end flat. Residuals between -6 to 6; Outlier now within 95% confidenceHowever, value 0 for x⁴

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.

Full Moon

First Order Polynomial (Linear)

P(x) = -2.8232x + 95.2369Degrees of Freedom: 9Norm of residuals: 14.0320

All data within 95% confidenceResiduals spread out at > phaseRange between-8 to 10

Second Order Polynomial

P(x) = -0.1101x² - 1.5609x + 92.1742

Degrees of Freedom: 8 Norm of residuals: 13.8883

All data within 95% confidenceResiduals spread out at > phaseRange smaller than 1st(-7 to 9)

Third Order Polynomial

P(x) = 0.0445x³ - 0.8622x² + 2.1771x + 87.0518

Degrees of Freedom: 7 Norm of residuals: 13.7597

All data within 95% confidenceResiduals spread out at > phaseRange similar to 2nd (-7 to 9)

Fourth Order Polynomial

P(x) = 0.0984x⁴-2.186x³ + 16.481x² - 50.848x + 137.769

Degrees of Freedom: 6 Norm of residuals: 12.5243

Interesting kinks to curve. Residuals look more randomRange slightly smaller.

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.