Statıstıcs Iı Deneme Sınavı Sorusu #1016162

Which of the following statements about Pearson's Correlation Coefficient is true? 


A relationship shown by Pearson’s correlation coefficient means that one variable’s existence is the cause of the second variable’s existence.

Pearson’s correlation coefficient isn't easily affected by the outliers.

In order to show the degree of the relationship between three or more continuous variables, The Pearson’s correlation coefficient is used.

Pearson’s correlation coefficient gets values between -1 and +1.

The positive sign of the correlation coefficint indicates that the change in the variables is in the different directions. 


Yanıt Açıklaması:

In order to show the degree of the relationship between two continuous variables, The Pearson’s correlation coefficient or Pearson’s product moment correlation coefficient is widely used. There are two symbols used for Pearson’s correlation coefficient, population correlation is represented by ? (rho) and sample correlation is represented by r. Pearson’s correlation coefficient gets values between -1 and +1. If the result is exactly -1 or +1 then there is a perfect relationship between the variables. The sign of the Pearson’s correlation coefficient indicates the direction of the relationship. The positive sign indicates that the change in the variables is in the same direction.The Pearson’s correlation coefficient is a very useful tool to show the degree of the linear relationship between two variables. The Pearson’s correlation coefficient is not a perfect tool, and we should be careful while using it. First of all, Pearson’s correlation coefficient does not show the causal relationship. A relationship shown by Pearson’s correlation coefficient does not necessarily mean that one variable’s existence is the cause of the second variable’s existence. There may always many known or un-known effects on the existence of a variable. Pearson’s correlation coefficient is easily affected by the outliers. In order to control this problem, careful examination inspection of the relationship with a scatterplot will be very helpful. If a data pair is identified as an outlier or as unusual observations, the researcher may investigate the reasons of the existence of these values in such a problem and may or may not include these data points in his/her investigation. The study of outliers a very detailed subject and unfortunately will not be explained in this chapter. At the moment it is enough for you to know that if there are outliers, then the Pearson’s correlation coefficient value may not be correct, and the results should be studied in caution. The correct answer is therefore D. 

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