Scatter plots, as demonstrated in Question #1, are useful for crude analysis of data. They can be used to demonstrate whether any type of association (i.e., linear, non-linear) exists between two continuous variables. Examples of continuous variables for which an association can be demonstrated are: arterial blood pressure and dietary salt consumption; blood glucose level and blood C-peptide level; etc. If a linear association is present, the correlation coefficient can be calculated to provide a numerical description of the linear association.
The correlation coefficient ranges from -1 to +1 and describes two important characteristics of an association: the strength and polarity. For example, in Question #1, graph A describes a strong positive association (as the value of one variable increases the value of the other variable also increases) whereas graph D describes a strong negative association (as the value of one variable increases the value of the other variable decreases). Graph E describes a weaker positive association compared to graph A; you should expect a correlation coefficient around +0.5. Graphs B and C demonstrate no correlation because the value of one variable stays the same over the range of values of the other variable.
You can also calculate the coefficient of determination by squaring the correlation coefficient. The coefficient of determination expresses the percentage of the variability in the outcome factor that is explained by the predictor factor. In Question #3, the correlation coefficient is (-0.8); therefore, (-0.8)*(-0.8) = 0.64 (64%) of variability in plasma homocysteine level is explained by folic acid intake.
It is important to note that a correlation coefficient describes a linear association but it does not necessarily imply causation. This explains why answer choice D is superior to choice C in Question #2.