Correlation and what it tells me

Question

OK, I need a little help here. I have attached two pictures; Data and Chart in which the data shows a correlation coefficient of 0.283168 which was calculated by Excel. Can someone please tell me what this calculation actually tells me? Really curious as I am trying to learn this.

Let me add a little more information to this. The column showing RATES is the Federal Fund Rates and each rate corresponds with the number of sales of homes while at that rate. Normally, when the Federal rate is higher, sales generally are lower however this is not the case in this example. With this new information in mind, what does the data show in relation to the correlation coefficient. Thanks in advance, this is all new to me.

Answer 1

The correlation coefficient is a measure of how well a (straight) line could be fitted to match the data. If it is 1, then the number of sales is directly proportinal to the the rates. The closer the value is to 0, the more they deviate from the line.

See for example http://upload.wikimedia.org/wikipedia/commons/8/86/Correlation_coefficient.gif

Answer 2

It tells you that $28.3168$% of the variation in the dependent variable is explained by variation in the independent variable according to the given fitted equation. Assuming that the dependent variable is Sales, the fitted equation is probably linear and so of the form $R=aS$ for some constant $a$.

Answer 3

The correlation is a measure of the strength of a linear relationship between two variables. Around .28 is a weak relationship, and thanks to the graph we can see why - there are two sales values that ruin what would otherwise be a strong relationship (if the two strange ones weren't there, then the correlation would be .9949, a VERY strong linear relationship).

The other poster's explaination regarding what is explained by the other variable is seemingly mistaking correlation for R-Squared. The R-Squared value for this (as we only have two variables here) is simply the square of the correlation, or 0.0802. That being said, it is actually 8.02% of the variation in sales that can be explained by rates (Again, this would be much higher if it weren't for those two out of line observations).