This may not be the best thread for this, but as this is based on UN23-33, ...

Remember that the (linear) correlation coefficient between 2 statistical variables has a value between -1 and +1.

A correlation coefficient whose absolute value is greater than .8 is generally considered high.

A correlation coefficient whose absolute value is smaller than .5 is generally considered low (which means that there is no meaningful correlation between the two variables - the angle between the 2 variables is > 45°).

As an example, correlation coefficients between astrological signs and typical traits of personality usually associated with them have been evaluated as .4. Sorry for those who thought astrology was a science.

Here are a few results about correlation coefficients based on UN23-33 (currently the only list for which I have the necessary data).

As this list of puzzles is short, the following should be taken with some care. In particular, as all these puzzles are in my levels 4 to 8 (hard to hyper-diabolical for a human player), I don't kow if these results can be extended to lower levels (higher levels are likely to be beyond a normal human player's capacities).

Remember that the level of a puzzle in my classification is the length of the longest chain necessary to solve it (using my set of rules - i.e. basic rules + nrczt chains)

Results in my approach:

My-levels vs My-computation-times: .887

My-levels vs My-memory-requirements: .791

My-computation-times vs My-memory-requirements: .953

Notice that although there is such a statistical correlation between level and time or memory, time or memory can't be used to define the level of an individual puzzle: these results are valid only statistically.

Comparisons:

My-levels vs Champagne-levels (Champagne's level 1+ given value 1.75): 0.67

My-levels vs Champagne-levels (Champagne's level 1+ given value 1.5): 0.822

My-levels vs Champagne-levels (Champagne's level 1+ given value 1.25): 0.834

My-levels vs Champagne-levels (Champagne's level 1+ given value 1): 0.82

Champagne-levels vs Champagne-computation-times: 0.785 (Champagne's level 1+ given value 1.5)

It'd be interesting to compute the correlations with ER, but I have no means of computing ER. If anyone can do it for each of these puzzles, I'll do the complementary statistical computations.

It'd be interesting also to compute such correlations for a longer list of puzzles, but this may require a lot of work (computation times and memory requirements are not recorded in the current version of SudoRules).

If anyone is interested, please let me know, so that we can chose a reference collection of puzzles. I think 1000 random minimal puzzles would be enough (unless we concentrate on exceptionally hard ones).