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The correlation coefficient, plus graphical methods to verify the validity of a linear relationship (which is what the correlation coefficient measures), and the appropriate tests of the statisitical significance of the correlation coefficient.
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Correlation is a measure of the degree of agreement in the changes (variances) in two or more variables. In the case of two variables, if one of them increases by the same amount for a unit increase in the other, then the correlation coefficient is +1. If one of them decreases by the same amount for a unit increase in the other, then the correlation coefficient is -1. Lesser agreement results in an intermediate value. Regression involves estimating or quantifying this relationship. It is very important to remember that correlation and regression measure only the linear relationship between variables. A symmetrical relationshup, for example, y = x2 between values of x with equal magnitudes (-a < x < a), has a correlation coefficient of 0, and the regression line will be a horizontal line. Also, a relationship found using correlation or regression need not be causal.
There are both advantages and disadvantages of data collection methods in statistics. The main advantages are the metrics and correlation one can draw from statistics. The disadvantages stem from sampling errors.
Estimating one of them is equivalent to estimating the other.