For this study, I am using an econometrics program called eviews. To learn how to interpret my results, please read my original article doing the same thing for skaters here.
Data:
I am using goalie attributes and statistics from each individual season between seasons 64 and 73. While I ideally would like to use more seasons to get more data, all seasons before season 64 do not have the search function to look for all goalie attributes. Instead, I need to go into each individual team for their goalie stats and this exponentially increases the time I need to collect attributes, and ain't nobody got time for that. If anyone were to kindly provide me this info I could run these results again, otherwise we will go with what we got.
VHL Regression Results:
The adjusted R^2 for all VHL stats and attributes is not great, as this means that 42% of the variation in the dependent variable, save percentage, is explained by the variation in the independent variables (attributes). Ideally you want the adjusted R^2 to be higher than this. This could mean that perhaps a lot of save percentage does come down to either team performance around the goalie or just sim luck in the sim deciding if it likes your goalie or not. Going off of this, there are two statistically significant attributes of note - reaction time (8.7%) and size (8.7%), as you generally want your statistics to be under 10% probability in order to be significant. Reaction time appears to be the most important one to upgrade, as an increase of reaction time by 1 increases your save percentage by 0.04. This is in line with @GustavMattias's guide to building, as reaction time is one of the four generally accepted goalie attributes to upgrade. According to this, I would prioritize it first. Next up, size is the only other statistically significant attribute, with an increase in size by one increasing your save percentage by 0.016. I would use this info to make size my 5th most prioritized attribute, after the big four.
VHLM Regression Results:
The adjusted R^2 for the VHLM results is way higher, with 71% of the variation in the dependent variable, save percentage, explained by the variation in the independent variables (attributes). The only statistically significant attribute according to this is handspeed, which also has the highest coefficient. An increase in hand speed by one increases a goalie's save percentage by 0.07, which is quite a lot. The next closest attribute to being statistically significant is size, which has showed up again.
Quick Summary:
According to the previously agreed upon tiers in Gustav's builder article along with the information here, I would order goalie attributes as such:
1) Hand speed
2) Reaction Time
3/4) Rebound Control
3/4) Style Control
5) Size
6/7) Skating
6/7) Agility