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The calculation of the product-moment correlation coefficient is such that it will lie between 1 and -1, with 1 meaning that there is perfect positive correlation, 0 no correlation and -1 perfect negative correlation. From the above values, we can clearly see that the link between ability in Science and in Maths is greater for the male students than the female students since the males' coefficient is far closer to 1 than the females. Therefore, while the relationship between Maths and Science for both the males and females is positive correlation, there is clearly a greater link between ability in these two subjects for the males than for the females. I have now addressed the second of my earlier statements, but have yet to confirm that, on average, both the male and female students showed greater ability in Science than in Maths. Flicking on through the A' Level Statistics book, I see that the line of best fit I would normally draw by inspection can actually be calculated. We call this calculated line the least squares regression line. I will now calculate such a line for the males and then for the females, and compare these lines to the line, y = x. If the students were of a truly equal ability in Maths and Science, then the line of best fit for the scatter diagram would fit the equation, y = x where Maths is the x-axis and Science is the y-axis. However, as seen, the students are not all of an equal ability in Maths and Science, and therefore the production of a least squares regression line which is above the y = x would confirm that the students, on average, showed a greater ability in Science than in Maths. Below is a table to show the result of my calculations:
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