You should probably start by getting a general idea about the relationship between Tonnes and Density:
plot(Tonnes~Density)
lines(ksmooth(Density,Tonnes,bandwidth=0.5))
and playing with the bandwidth parameter to figure out the form of the mean function of Tonnes conditional on Density. If it is anything like linear, you should be fine with regression/ANOVA techniques - e.g. R-squared given by the summary(lm(Tonnes~Density)) is precisely the portion of the variance in Tonnes due to the variance in Density. Look up the details here: http://cran.r-project.org/doc/contrib/Faraway-PRA.pdf
If it is nonlinear, some transformation of variables or nonlinear regression modelling might be in order and it is hard to specify a general approach here so maybe you should come back with a plot.
The short answer, no, at least to my knowledge.
I think you are confused about a few things here including what a contingency table is. A contingency table is nothing more than a table that displays frequency distributions. When you refer to TP,FP,TN,&FN you are referring to a hat you describe is a special contingency table known as a confusion matrix. A confusion matrix is (in binary situations) a 2x2 matrix containing the predicted group memberships. For example:
A B A B
A 5 2 A TP FP
B 3 8 B FN TN
This is typically used to evaluate the performance of a predictive algorithm. In this case there are 5 true positives, 2 false positives, 3 false negatives, and 8 true negatives. You can ultimately use this table to derive many other statistics (e.g. Accuracy, Kappa, Sensitivity, etc).
The generic contingency table is simply a representation of the distribution of groups in a population. For example (copying from wikipedia):
Right-handed Left-handed Total
Males 43 9 52
Females 44 4 48
Total 87 13 100
Now, this is, more-or-less, raw data that you can use to test a hypothesis. Assuming the data fits some assumptions, some tests include chi-squared, fisher's, and the G-test among others.
This is different from ANOVA (which in this case would be two-way). ANOVA uses some quantitative value as opposed to just counts. Your output is intended to be used to interpret how the quantitative variable is impacted by the factor.
Best Answer
Think about how many degrees of freedom there must be (total, residual & regression). Then you can work backwards from the $MSE$ to get the missing $SS$s.