Add more regression operations

[MithicSpirit]

Under Statistics > Regression the only options are for correlation and not regression (pearson's correlation coefficient, spearman's rho, and the statistical correlation; see https://qalculate.github.io/manual/qalculate-definitions-functions.html#qalculate-definitions-functions-2-Regression). It would be nice if there were actual regression options there such as linear regression and other forms.

[hanna-kn]

I will change the category title (I do not why it has that title—it hasn't changed in 15 years) and look into the possibility of adding functions for actual regression.

[MithicSpirit]

I've been thinking and a possible issue is that regression would need to output a function, which I am not sure is currently possible. Another other option would be to have a function for each value for each regression method (e.g. slope, y-intercept for linear regression), or a single function per regression method that returns a vector of the values.

EDIT: I think that it would be possible to output a function if one of the inputs was the independent variable itself, or if a specific value is passed in the regression is just computed at that value.

[hanna-kn]

A function for linear regression could be defined using covar(\x,\y)/varp(\x)×(x−mean(\x))+mean(\y). This would return an expression with format ax + b. It can be extended to support a single argument and possibly return a confidence interval ((a±c)x + b±d).

[MithicSpirit]

While confidence intervals would certainly be nice to have, they might be a bit outside of the scope of a calculator and instead better suited for statistical analysis software like JASP.