The line of best fit (*y = mx + b*) is
computed from a random sample of measurements of *x* and *y*. If we
used a different data set we would most likely compute slightly different
values for the *m* and *b* parameter. Thus our values are always
estimates and as such have a confidence interval associated with them.

The confidence interval for the predicted *y
*value for a given value of the independent variable *x* is computed
using: _{}

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

*for the mean response*.
Thus in row 28 we are finding the confidence level associated will *all*
measurements with x = 100.

The notes above show how to compute the
confidence level for the *y*-values
that are predicted by fitting the measures *x*-
and *y*-values. Having made such a fit,
we might use the results to predict the *y*-value
associated with a *new* *x*-value.
*y*_{new} = *a* + *bx*_{new} ± t_{α,df}SE(y_{new}).
For this calculation we use: _{}; the additional term of 1 within the square root makes this
confidence interval wider than for the previous case.

The notes *Regression Analysis –
Confidence Level for a Measured X *are more applicable when you are using a
calibration curve to find *x* when *y* is measured.