I need to perform a two-step calibration and I need you to tell me if I do that correctly. First I want to calibrate a force sensor with masses. I measure several weights and perform a linear regression of my data such as:

$F_1 = a_1 s_1+b_1$

with $F_1$ the applied force in N, $s_1$ the sensor value and $a_1$ ans $b_1$ the regression parameters.

It is easy to estimate a confidence interval for $F_1$ from:

$\sigma_{F_1}=\sqrt{\frac{\sum{(F_1-(a_1s_1+b_1))^2}}{N-1}}$

But then it starts to get tricky for me. I use the force sensor to calibrate another force sensor on a machine. I perform the same type of experiment with different loads, and I want to perform a linear regression such as:

$F_1 = a_2 s_2+b_2$

with $F_1$ the measured force with the force sensor, $s_2$ the sensor value of the machine and $a_2$ ans $b_2$ the regression parameters. So I already know $\sigma_{F_1}$, how can I get a confidence interval of a single $s_2$ measure  ?

I need to perform a two-step calibration and I need you to tell me if I am doing that correctly. First I want to calibrate a force sensor with masses. I measure several weights and perform a linear regression of my data such as: $$ F_1 = a_1 s_1+b_1 $$ with $F_1$ the applied force in N, $s_1$ the sensor value and $a_1$ and $b_1$ the regression parameters.

It is easy to estimate a confidence interval for $F_1$ from: $$ \sigma_{F_1}=\sqrt{\frac{\sum{(F_1-(a_1s_1+b_1))^2}}{N-1}} $$ But then it starts to get tricky for me. I use the force sensor to calibrate another force sensor on a machine. I perform the same type of experiment with different loads, and I want to perform a linear regression such as: $$ F_1 = a_2 s_2+b_2 $$ with $F_1$ the measured force with the force sensor, $s_2$ the sensor value of the machine and $a_2$ ans $b_2$ the regression parameters. So I already know $\sigma_{F_1}$, how can I get a confidence interval of a single $s_2$ measure?