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How to calculate uncertainty of linear regression slope?
Responding to “I’m trying to find how much k and n in y = k x + n can change but still fit the data if we know uncertainty in y values.”
When do X and Y each have uncertainties?
X and Y both have some noise associated with them due to measurement inaccuracy however the relationship of the underlying true values (i.e. if we could remove the noises) of these points should be of the form y = m x + c where m and c are constants.
Which is a special case of Deming regression?
In both cases you want to use Deming regression. Case 1 is a special case of Deming regression called orthogonal regression, which minimizes the sum of squared perpendicular distances from the data points to the regression line. For case 2, the general case, you will need an estimate of the ratio δ = σ y 2 / σ x 2 for the problem to be solvable.
How is measuremet error used in Deming regression?
Measuremet error shrinks coefficient of the right-hand-side variable measured with an error towards zero. It causes not uncertainty of an estimator, but its inconsistency instead. While mentioned in other answer deming regression is two-variable concept, the multivariate solutions include instrumental variable method as preferred option.
What is the slope of a trend line in Excel?
In Excel, you could fit a trendline. Or, you could draw a best fit line. Either way, I would get something like this (I did this in Logger Pro): This gives a slope of 3.28 (compare to pi = 3.14). I could get a better slope if I required the fitting function to go through the origin (0,0), but I am not going to do that.
Is there a way to calculate the slope of a line?
Basically, if you draw a best fit line you could “wiggle” the line and still have it fit. This would give a minimum and a maximum slope. If you do the trendline in Excel, I am not sure how you would do this. If you do it by hand on graph paper, it would be easy.