Title: Conclusion
Course: UGQuants (SSPS) > Section: Correlation and Regression

Conclusion

In this module we have looked at two essential ways of looking at the relationship between two variables: correlation and regression. Although they are related it is important to keep them distinct and get a clear idea of the difference between the two.

Correlation tells us about the strength of the relationship, how closely our line fits the data we have and therefore how much of the variation of each variable is accounted for by the variation in the other. If our datapoints cluster close to our line then we have a strong relationship. Knowing the value of one variable tells us a lot about the probable value of the other variable. Alternatively, if our variables are only weakly related, knowing the value of one variable may be a poor guide to the value of the other.

Regression is a way of summarising the form of the relationship, which works by fitting a line to the points in a scatterplot minimising the sum of the squared vertical distances between the actual values of Y and the line. It can help us to summarise the form of a relationship between two variables: does the value of one variable tend to increase or decrease as the value of the other increases?, for example. Our regression equation, which our fitted line represents graphically, is a simple model of the relationship.

Finally both these methods work only if we can sensibly use a straight line to approximate our data (in other words if there is a linear relationship).

After working through this module you should have learned:

1 | What a scatterplot comprises: the X axis, Y axis and coordinates
2 | What is meant by a linear relationship
3 | What is meant by the strength of a relationship between two variables
4 | How the strength of a relationship between two variables can be summarised by a correlation coefficient.
5 | How to calculate the covariance and the Pearson product moment correlation coefficient, r, for a pair of variables, and how to use the software to do this.
6 | That without correlation there is no causation, but that the reverse is not the case. The existence of correlation or association is never in itself proof of causation.
7 | What a regression line is, and the equation that describes it: Y = a + bX + e
8 | What it means to fit a regression line that minimises the sum of the squared residuals (OLS regression)
9 | What is meant by the intercept (a) and the slope (b) of a regression line
10 | How to calculate a regression equation, or use the software to do this for you
11 | What the coefficient of determination, R^2, means