Does anyone know what a correlation coeeficient (r squared) is??
I am writing up a lab report and am not really sure how it relateds to errors etc

Grab a statistics text from the library, and look up correlation coefficient in the index.

Or, look here:
MathWorld (http://mathworld.wolfram.com/CorrelationCoefficient.html)
http://mathworld.wolfram.com/c3img413.gif

You can see from the image that the correlation coefficient describes how well the data fits the regression line.

I think that more data points and smaller errors should produce a higher correlation coefficient, if a linear relationship exists. A low correlation coefficient indicates not enough data, large errors, a non-linear relationship, or no relationship.

Covariance of two random variables is average of product - product of averages. Correlation coefficient is covararice divided by product of standard deviations.