I'm studying the example H.3 from this Standard, regarding the expression of the uncertainty in measurement, but I cannot understand from where the formula (H.13e) comes.
My problem is to find the correlation formula between the slope $m$ and the intercept $q$ of a generic regression line like: $\hat{y} = b(x) + a$
I thought the formula to be used for the correlation was (according to this example from Wikipedia) $$ r(b,a) = \dfrac{nS_{xy} - S_xS_y}{\sqrt{(nS_{xx} - S_x^2)(nS_{yy} - S_y^2)}} $$ but it gives me the value: $r = 0.737$ instead of $r = -0.930$
The values that I'm using are:
| x | y |
| - | - |
| 1.521 | -0.171 |
| 2.012 | -0.169 |
| 2.512 | -0.166 |
| 3.003 | -0.159 |
| 3.507 | -0.164 |
| 3.999 | -0.165 |
| 4.513 | -0.156 |
| 5.002 | -0.157 |
| 5.503 | -0.159 |
| 6.010 | -0.161 |
| 6.511 | -0.160 |
