Consider the case where a number of
observations (*n*) are used to calibrate an instrument. The dependent
quantity (*x _{i}*) is varied and the independent quantity (

We would begin by fitting the calibration
data to a line of best fit – generally a linear relationship (*y = mx + b*)
is used. We may now use *x = (y – b)/m* to discover the value of the
unknown sample which records a value of y on the instrument. Frequently we
would make a number of repeated measurements of y with the unknown sample. Let *k*
be the number of repeated measurements (this may, of course, be 1)

However, there is an uncertainty associated
with the calibration curve and we wish to report a confidence interval with the
computed *x* value. The confidence interval for the predicted *x *value
for a given value of the independent variable *x* is computed using
either:

_{} or _{}

where *t* is the critical t statistic,
*S _{yx}* the standard error of the estimate,

The labels *x, y* and *YY* are
used to name the data A3:A7, B3:B7 and A14:A18, respectively. The labels in
E2:E16 are used to name the cells to their right.

The cells F2:F9 are used to compute values from the calibration data (A1:B7) while in cells F12:F18 we computed values associated with data on the “unknown” sample. Note that the experimenter made 5 duplicate measures on the sample. In F16 and F17 we have two formulas to show that the equation shown above are indeed equivalent. The symbol ± is produced with the keystrokes ALT+0177; the numbers must be typed on the numeric keypad.