# What exactly is the "proportion of variability explained"?

One often hears to say "more than 70% variability is explained by ..." What exactly is meant by this? Th proportion of the sum of squares (SSE), or mean sum of squares (MSE)? For example in the following anova table:

                                    Df Sum Sq Mean Sq F value Pr(>F)
as.factor(site)                    444   8357   18.82   163.1 <2e-16 ***
as.factor(year)                     12    569   47.43   410.9 <2e-16 ***
as.factor(month)                     5    863  172.53  1494.8 <2e-16 ***
as.factor(year):as.factor(month)    60    769   12.82   111.1 <2e-16 ***
Residuals                        34188   3946    0.12
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
7176 observations deleted due to missingness


could we say that most of the variability was explained by site? We see that site covers most of the SSE but as there is a lot of sites, the MSE for site is almost the lowest in the table.

And how would I interpret this in practice? I want to know where is the variability, whether it varies mostly accross time or space. Is the site actually the biggest source of variability, or is it a month and year? Shall I read SSE or MSE column for this purpose?

PS: please note I am not a professional statistician, so if you are about to respond with a lot of math then please make also some simple summary for dummies :-)

• possible duplicates Aug 2, 2013 at 17:55
• my question is not purely technical as the linked one; it has a bit of the interpretational/philosophical level. I don't stick to particular technology like anova; I try to find proper means to answer my question. Aug 2, 2013 at 19:30
• you use % in SSE but not in MSE which is what you are looking in the first part of the question. Aug 2, 2013 at 19:34
• Thanks @Metrics! And what do you think is more appropriate to consider, if I want to answer the question whether my variable varies mostly in time or in space (i.e. accross sites)? Aug 2, 2013 at 20:13
• I think it should be site/space since SSE is higher for that. Aug 2, 2013 at 20:16