When you are investigating the relationship between two cont

When you are investigating the relationship between two continuous random variables, why is it important to create a scatter plot of the data? What are the strengths and limitations of Pearson?s correlation coefficient? How does Spearman\'s rank correlation differ from the Pearson correlation?

Solution

you need to create a scatter plot of the data for you can see the regression or the data behavior of the investigations and you can conclude about if there is a similarity between data

The correlation coefficient is a numerical way to quantify the relationship between two variables, e.g. X and Y and it is denoted by the symbol R. The corelation coefficient is always between -1 and 1, thus -1 < R < 1.
If the correlation coefficient, R, is positive, then a increase in X would result in a increase in Y, however if R was negative, an increase in X would result in a decrease in Y. Larger correlation coefficients, such as 0.8 would suggest a stronger relationship between the variables, whilst figures like 0.3 would suggest weaker ones.

Disadvantages of the correlation coefficient are that it only measures linear relationhips between X and Y and for any relationship to exist, any change in X has to have a constant proportional change in Y. If the relationship is not linear then the result is inaccurate. In addition to this the correlation is meaningless if it is about categorical data, such as hair colour or gender.

similar to the Pearson product moment correlation coefficient, Spearman’s correlation coefficient can be 0 for variables that are related in a non-monotonic manner. At the same time, unlike the Pearson’s correlation coefficient, Spearman’s coefficient can be 1 not only for linearly related variables, but also for the variables that are related according to some type of non-linear but monotonic relationship