Scatter plot : Are the two observed data related

Question

I have a regression question that ask to draw the scattered plot graph and then conclude if the two data lists are related.

The two data lists are years of people and their cholesterol level.

I went on and drawed it in excel to get a better idea of whats going on and got this :

My conclusion is that yes indeed the two data lists are related because all the points are very close. but that seems kind of weak as a proof 'the points are very close...' seems objective to me.

Am I missing something here ?

The two data lists are years of people and their cholesterol level.

Answer 1

You are not missing anything. As you observed from the plot, at least globally, older is the person, higher is his/her cholesterol level. As a first (and probably very good) approximation, a linear model as the one you used with Excel explains most of the phenomena.

Answer 2

Yes, "very close" is subjective. An objective measure of the relationship would be the correlation coefficient. You should be able to get Excel to output this as $R^2$ or something. Then you can say "the variables are 90% correlated" or whatever, and the reader can make up his or her own mind about how related they actually are.

I get about $95.57\%$ using Matlab's "corrcoef" function.

Answer 3

Another thing you could try to calculate is the correlation coefficient of the two datasets (see this link). It measures 'how linearly dependent' the two samples are. For example, it equals $1$ if one variable is linearly dependent on the other and $0$ if they are not linearly dependent.