york_fit() calculates the regression parameters of
an error-considering linear regression.
Arguments
- x
vector of x values.
- y
vector of y values. Has to be same the length as x.
- x_err
Error on the x values. Has to be same the length as x.
- y_err
Error on the y values. Has to be same the length as x.
- r
Correlation coefficient of x_err and y_err at each data point. Default:
0(independent errors). Has to be same the length as x. Optional.
Value
A list with regression parameters:
slope and its standard error
intercept and its standard error
weights of the points (normalized to 1)
residual standard error (sigma)
R2
p-value (two-tailed t-test).
Details
Regression fitting method according to York et al. (2004). The algorithm is described in the appendix of Wacker et al. (2014).
References
York, D., Evensen, N. M., López Martínez, M., & De Basabe Delgado, J. (2004). Unified equations for the slope, intercept, and standard errors of the best straight line. American Journal of Physics, 72(3), 367-375. doi:10.1119/1.1632486
Wacker, U., Fiebig, J., Tödter, J., Schöne, B. R., Bahr, A., Friedrich, O., et al. (2014). Empirical calibration of the clumped isotope paleothermometer using calcites of various origins. Geochimica et Cosmochimica Acta, 141, 127-144. doi:10.1016/j.gca.2014.06.004
Examples
york_fit(
x = c(1, 2, 3),
y = c(1.1, 1.9, 3.2),
x_err = c(0.1, 0.2, 0.1),
y_err = c(0.2, 0.1, 0.2))
#> $slope
#> [1] 1.061775
#>
#> $slope_se
#> [1] 0.1599487
#>
#> $intercept
#> [1] -0.05293936
#>
#> $intercept_se
#> [1] 0.3416549
#>
#> $w
#> [1] 0.3412216 0.3175568 0.3412216
#>
#> $sigma
#> [1] 0.1167873
#>
#> $R2
#> [1] 0.9822171
#>
#> $pval
#> [1] 0.09518642
#>