Experimental uncertainty (error) in using linear calibration
A typical set of linear data can be described by the plot of the absorbance, A, of a solution as a function of its concentration, C, in mg dm^{3}.
C / mg dm^{3}

0 
20 
40 
60 
80 
100 
120 
A

0 
0.267 
0.583 
0.824 
1.120 
1.313 
1.499 
A solution of unknown concentration gives 3 replicate measures of absorbance: 0.763, 0.741 and 0.749, and we use the calibration data to calculate a bestestimate for the true concentration of this solution.
The calculation uses the BeerLambert law that states that, for low concentrations, the absorbance is proportional to concentration. This means that we would expect that plotting absorbance against concentration should give a straight line.
This data is analysed using:
An analysis of Residuals and Corrrelation coefficients to  see video Beers Law v1
 Identify curvature of the calibration data at high concentrations (xvalues)
 Select an appropriate linear calibration range
Functions and equations to calculate  see video Beers Law v2
 Best estimate of the unknown concentration using both a freefit trendline and a trendline forced through the origin.
Functions and equations to calculate  see video Beers Law v3
 Standard uncertainty in the calculated concentration, given by
or
 95% Confidence Interval for the true value of the unknown concentration
(Refer to section 13.3.3 in the text: Essential Mathematics and Statistics for Science, 2nd Ed, by G Currell and A A Dowman)