In the Major Axis Regression is used the Pearson's correlation coefficient (r) or another correlation coefficient?

Question

I am using package in R (smatr) and applying major axis regression, I get a series of statistical values ​​but I don't understand the correlation coefficient (r) if it was calculated based on Pearson or based on another?

Here are my results:

Call: sma(formula = RPP2 ~ RPP1, data = dat, slope.test = 1) 

Fit using Standardized Major Axis 

------------------------------------------------------------
Coefficients:
             elevation     slope
estimate    -0.4426533 0.9489647
lower limit -0.6243337 0.9430954
upper limit -0.2609728 0.9548706

H0 : variables uncorrelated
R-squared : 0.86427 
P-value : < 2.22e-16 

------------------------------------------------------------
H0 : slope not different from 1 
Test statistic : r= -0.1408 with 13548 degrees of freedom under H0
P-value : < 2.22e-16 

Answer 1

From Warton et al. (2006. Bivariate line-fitting methods for allometry. Biol. Rev. 81):

To test if the true slope is equal to some value b, a simple approach to use is to test if the residual and axis scores are uncorrelated, when these are calculated using b as the slope.

The result r= -0.1408 refers to the slope test.

I think that the other test refers to the Pearson correlation coefficent. Try:

with(dat, cor.test(RPP2, RPP1)) # to obtain a P-value
with(dat, cor(RPP2, RPP1))^2 # to compare with R2 from sma()

You really need to study the methods before implementing them.