Types of correlation & what is correlation coefficient: Correlation and Regression part-1

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Finally got someone who can make me understand the correlation

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[@VGBGI]

Major points missing in this presentation 1. Any conclusion about correlation coefficient can be drawn only after finding the statistical significance of the correlation coefficient. Without finding statistical significance, no conclusions should be drawn. Only if the correlation coefficient however small or high may be, is statistically significant, at (n-2) degrees of freedom, conclusion can be drawn. 2. Pearsonian correlation coefficient measures only the strength of linear association between two continuous variables. Therefore unless the scatter diagram between the two continuous variables indicate some linear direction of association, correlation coefficient can be computed. Suppose the scatter between X and Y shows a curvilinear association such as inverted U or U or a curve, then correlation coefficient should not be computed in such cases. 3. The two variables X and Y should be continuous variables and not discrete variables. For example we cannot use Pearsonian correlation coefficient to measure the degree of association between Gender and Income, or between Sex (male, female, other) and Location (North, South, East, West) since they are discrete variables. 4. Pearsonian Correlation will not and cannot indicate causation. ie. if correlation between X and Y is negative as for example between quantity demanded and Price, we can only say that Price and Quantity demanded are moving in opposite direction; if correlation between Height and Weight is positive, we can only say that Height and weight are moving together in positive direction. But we can never say that as the price increases, quantity demanded decreases or vice versa. Similarly, we can never say that as the height increases, weight also increases. Therefore, kindly note that for using Pearsonian correlation both two variables under consideration must be continuous variables. For example Gender is a discrete variable (since it can be male, female or other). Income and age are continuous random variables and correlation can be measured between these two variables. Once again, kindly note that if the correlation between age and income is say 0.75 and is statistically significant, you cannot and should not say that as the age increases, income increases and so on, because Pearsonian correlation only indicates the degree of association between the two continuous variables but not the causation. Using Pearsonian correlation, if the correlation is positive and significant, one should not conclude that as the variable X increases Y also increases; if the correlation is negative and significant, one should not conclude that as the variable X increases, Y decreases. One can only say for positive and significant correlation, X and Y are positively associated; and for negative and significant correlation, X and Y are negatively associated, but never conclude about causation. This is a common mistake found in many research articles which should be avoided. Kindly read Damodar Gujrati, Econometrics for all details.

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