Aside from the ksmooth approach you could do a simple linear regression:

fitted_model <- lm(Tonnes ~ Density)
summary(fitted_model)

In the summary you look for the "Estimate" that tells you how much increase you expect for each increase in Density.

You should also plot the model by simply:

plot(Tonnes, Density)
abline(fitted_model)

The plot tells you visually how well the line fits but it also hints if you need some value transformation. Log() is a good transformation that is frequently used, our sense of numbers is actually logarithmic and it's when we're about 3-4 years old that we unlearn that natural instinct of logarithmic counting. This is probably due to that many things appear logarithmic in nature, when a cell divides it divides into to creating an exponential increase in cells. You should suspect logarithmic transformations if your data is grouped at one end of the plot.

Aside from the ksmooth approach you could do a simple linear regression:

fitted_model <- lm(Tonnes ~ Density)
summary(fitted_model)

In the summary you look for the "Estimate" that tells you how much increase you expect for each increase in Density.

You should also plot the model by simply:

plot(Tonnes, Density)
abline(fitted_model)

The plot tells you visually how well the line fits but it also hints if you need some value transformation. Log() is a good transformation that is frequently used, our sense of numbers is actually logarithmic and it's when we're about 3-4 years old that we unlearn that natural instinct of logarithmic counting. This is probably due to that many things appear logarithmic in nature, when a cell divides it divides into to creating an exponential increase in cells. You should suspect logarithmic transformations if your data is grouped at one end of the plot.

@rolando2: I heard about the logarithmic counting through listening to a lovely RadioLab episode about Numbers. They report about tribes in the Amazon that don't have our numbers and that they still as adults count in a logarithmic way.