org-table, how to compute Coefficient of Determination between two time fields?

Question

I have two time fields. My productivity and sleep. I would like to run a Coefficient-Determination (As described here: http://www.r-tutor.com/elementary-statistics/simple-linear-regression/coefficient-determination )

Is it possible in org-mode?

E.g

|Date | productivity | sleep|
|-----|--------------|------|
|[meh]| 4:00         | 8:00 |

Answer 1

My previous answer was just too convoluted (and it didn't actually compute what OP wanted). It appears there's a much simpler way to do it:

This is actually the way to do it

| Date  | sleep | productivity | determination coefficient |
|-------+-------+--------------+---------------------------|
| [meh] |  7.50 |         4.00 |                           |
| [meh] |  8.00 |         5.00 |                           |
| [meh] |  8.50 |         6.00 |                           |
| [meh] |  8.00 |         4.00 |                           |
| [meh] |  8.20 |         5.00 |                           |
| [meh] |  8.70 |         6.00 |                           |
|-------+-------+--------------+---------------------------|
|       |       |              |                0.89847792 |
|       |       |              |                0.89847792 |
#+TBLFM: @9$4=vcorr(@2$2..@7$2, @2$3..@7$3)
#+TBLFM: @8$4=vpcov(@2$2..@7$2, @2$3..@7$3)/(vpsdev(@2$2..@7$2)*vpsdev(@2$3..@7$3))

As suggested by the comments. Note that this gives you r, whereas RUserPassingBy's results give r^2 (but, finally, both results are correct).

Answer 2

if you calculate R^2 by R within org-mode and Babel, it's very simple.

#+CAPTION: My productivity and sleep
#+NAME: MY-TABLE
| Date    | sleep | productivity |
|---------+-------+--------------|
| ~[meh]~ |  7.50 |         4.00 |
| ~[meh]~ |  8.00 |         5.00 |
| ~[meh]~ |  8.50 |         6.00 |
| ~[meh]~ |  8.00 |         4.00 |
| ~[meh]~ |  8.20 |         5.00 |
| ~[meh]~ |  8.70 |         6.00 |

#+BEGIN_SRC R :session *R* :results output :exports results :var TMP=MY-TABLE[,1:2]
summary(lm(TMP))$r.squared
#+END_SRC

#+RESULTS:
: [1] 0.8072626

Answer 3

Here Emacs Calc is!

Org-table is based on Calc function. Calc function vcorr calculates a correlation coefficient among two vectors. Use vcorr with calc-eval in Emacs Lisp with Org-mode.

A Coefficient-Determination is the same as R-square. R-square for a simple regression analysis Y on X equals to a squared value of a correlation coefficient between X and Y.

#+CAPTION: My productivity and sleep
#+NAME: MY-TABLE
| Date    | sleep | productivity |
|---------+-------+--------------|
| ~[meh]~ |  7.50 |         4.00 |
| ~[meh]~ |  8.00 |         5.00 |
| ~[meh]~ |  8.50 |         6.00 |
| ~[meh]~ |  8.00 |         4.00 |
| ~[meh]~ |  8.20 |         5.00 |
| ~[meh]~ |  8.70 |         6.00 |

When importing lists from Org-table to Emacs Lisp, you can select rows and columns. :var TMP=MY-TABLE[,1:2] selects for whole rows, with 2nd and 3rd columns.

c.f. http://orgmode.org/manual/var.html

#+BEGIN_SRC emacs-lisp :results value :exports both :var TMP=MY-TABLE[,1:2]
(require 'cl)                             ;; required for (first) and (second) function.
(setq LST (cddr TMP))                     ;; import data to list LST excluding column names and hline.
(setq VEC (apply #'mapcar* #'vector LST)) ;; transpose and change to vector VEC, as Calc accepts vectors only.
(setq X (first VEC))                      ;; X is a vector of sleep ('car').
(setq Y (second VEC))                     ;; Y is a vector or productivity ('cadr').
(setq VALUE-R                             ;; correlation coefficient.
  (string-to-number                   ;; calc-eval returns string.
   (calc-eval (format "vcorr(%s,%s)" X Y)))) ;; alas, calc-eval accepts only strings.
(setq VALUE-R2 (* VALUE-R VALUE-R))       ;; R-square for a simple regression
#+END_SRC

#+RESULTS:
: 0.8072625698326307

Answer 4

And of course you have the orgtbl-aggregate package (available on Melpa). It uses Calc as its backend engine. The vcorr function is the one to use, as wvxvw and RUserPassingBy put it.

#+BEGIN: aggregate :table "MY-TABLE" :cols "vcorr(sleep,productivity)"
| vcorr(sleep,productivity) |
|---------------------------|
|            0.898477918389 |
#+END: