At some point in your exploration you will need to plot a scatter graph. A scatter graph can show you whether there is any correlation between 2 variables. Just looking at the table of data you cannot always see if there is a trend, so we plot a scatter graph. Using a spreadsheet or your graphical calculator you can very quickly plot a graph, calculate the correlation coefficient (r) and draw the line of best fit. In your exploration you will need to show that you understand the calculations in depth, so you will need to calculate the r value and the line of best fit 'by hand'. You can however use technology to check you are doing the right thing as you go.
TI84 
Spreadsheet 
There is a great explanation of covariance on myimaths.com. There are a number of simple steps to follow:
 Work out the mean of x and then the mean of y
 Subtract the mean of x from each x value
 Subtract the mean of y from each y value
 Multiply the value from step 2 and 3.
 Sum every value on the final column
 Divide by how many pairs of data (n)
Line number 1: (31  53)x(50  46) = 88
Line number 2: (21  53)x(50  46) = 704
Line number 3: (78  53)x(60  46) = 350
etc...
Line number 2: (21  53)x(50  46) = 704
Line number 3: (78  53)x(60  46) = 350
etc...
The sum of 88 + 704 + 350 ... +..... is 3791 and there are 10 data pairs so we calculate 3791 ÷ 10 = 379.1.
You will need the standard deviation of both of your variables, again a good method for this can be found on myimaths.com or mathisfun.com.

Pearson's Product Moment Correlarion Coefficient
Calculating the 'linear regression equation of y on x' (equation of the line of best fit) is important so that we can estimate y when given x. It is important we stick with interpolation so as we can be reasonably sure of the accuracy or appropriateness of the result. Extrapolation falls outside of our measured data points and is illustrated in the diagram to the right. (Diagram source: http://upload.wikimedia.org/wikibooks/en/a/a2/NM19_103.gif)
