Uncertainty from linear fit on additional data Let's say I have 5 known data points with coordinates
$X$ : Area under curve
$Y$ : Activity
The 5 points have individual error ($\Delta X_{i}$,$\Delta Y_{i}$) on both $X$ and $Y$ and I know that the best fit of these 5 points is a linear fit.
After plotting my 5 original points, I have another one that I only know the Area under curve and not the activity.
With the fit equation of my 5 original points, I can associate an Activity to my 6th point.
Is there a way to provide a uncertainty to my 6th point ?
I have some ideas about Max/Min slopes but I don't know if it's the best way in this situation... And I have to use only Excel at the request of someone.
Thank you !!
 A: UPD. What is written below works if you estimate a line with least-squares estimation for regression model $Y = aX + b$ (that is the default in Excel). If you use different model and/or method to minimize errors both in $X$ and $Y$ - the answer is not correct.

What is a general procedure in this case is to write your model like this:

$Y = aX + b + \epsilon$

Where $a$ and $b$ are the coefficients you obtain by training your model, and $\epsilon$ is a noise. Usually it is assumed to be zero-mean and depending on unknown parameter $\sigma$. If you build your linear approximation with standart tools, it probably assumes that the noise is Gaussian $\epsilon$ ~ $N(0, \sigma)$.
So what you can do is to evaluate estimation for parameter

$\hat{\sigma^2} = \frac{1}{N}\sum_{i=1}^N(Y_i - \hat{Y_i})$

Where $N$ - number of your points, and $\hat{Y_i} = aX_i + b$ - your prediction.
If you do that, you can get confidence intervals as quantiles of $N(0, \sigma)$. For example, 95% confidence interval is approximately $[\hat{Y}_{new} - 1.96*\sigma; \hat{Y}_{new} + 1.96*\sigma]$.
You can do that with Excel.
More on mean squared error minimisation and linear regression is online.
