I am using an R package called BSL (Bare soil line), package is at https://rdrr.io/cran/landsat/man/BSL.html. The BSL package uses R's lmodel2 function (https://cran.r-project.org/web/packages/lmodel2/vignettes/mod2user.pdf) to build the model II regression.
The soil line is a linear relationship between reflectance values between Red and Near-infrared wavelengths and is defined by the equation: NIR = αRed + β where NIR and Red correspond to the near-infrared and red bands of the satellite image, alpha is the slope, and beta the y intercept.
I've used it successfully to create a regression line from the satellite image of my soil study area. It is Model II regression because there is error in the NIR and Red values, and I am using the MA (major axis) method to calculate the regression (see output below). For my research, I have difficulty determining if the y-intercept β is significant or not. I know the hypothesis test to determine if the Y intercept is significant: H0:ß=0 H1:ß≠0
For example, the BSL package generates this output, but it doesn't provide any statistical test (e.g. P-value) to to determine if the Y intercept is significant:
> result.bsl$BSL Intercept Slope 1323.007184 0.640505 > result.bsl$summary Model II regression Call: lmodel2(formula = bsl.joint[ratio43 < quantile(ratio43, llimit), 2]~ bsl.joint[ratio43 < quantile(ratio43, llimit), 1]) n = 3 r = 0.9878535 r-square = 0.9758546 Parametric P-values: 2-tailed = 0.09932547 1-tailed = 0.04966273 Angle between the two OLS regression lines = 0.6373716 degrees Regression results Method Intercept Slope Angle (degrees) P-perm (1-tailed) 1 OLS 1350.359 0.6359507 32.45435 NA 2 MA 1323.007 0.6405050 32.63976 NA 3 SMA 1303.397 0.6437702 32.77223 NA Confidence intervals Method 2.5%-Intercept 97.5%-Intercept 2.5%-Slope 97.5%-Slope 1 OLS -6286.498 8987.216 -0.6351029 1.907004 2 MA 48805.536 9004.094 -0.6384682 -7.265783 3 SMA -11020.651 4246.396 0.1537332 2.695840 Eigenvalues: 66506.64 336.0233 H statistic used for computing C.I. of MA: 0.8240161
There is a Parametric P-value to determine regression significance, but no p-value to determine significance of the y-intercept. The confidence interval for the Intercept (48805.536, 9004.094) also is unclear to me. The above output is the only output that I get from the regression using lmodel2. I also read the lmodel2 user manual but it doesn't any useful info about determining the statistical significance of the y intercept. Can anyone help me determine statistical significance of the Y Intercept from the above output?