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What is correlation coefficient?

Updated: 4/28/2022
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8y ago

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'Correlation coefficient' means a statistic representing how closely two variables co-vary; it can vary from -1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation)

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A key piece of information that is left out of the answer by True Knowledge (which casts very serious doubts about its name!) is that the statistic only is a measure of linearrelationship. A symmetric non-linear relationship (a parabola, for example) will show zero correlation but show anyone a graph of a parabola and then try convincing them that there is no relationship between the two variables!
A correlation for two variables is a measure of the strength of a linear relationship between them. It is a measure that ranges from -1 (the variables move perfectly together but in opposite directions) to 1 (the variables move perfectly together and in the same direction). A correlation coefficient of 0 indicates no linear relationship between the variables.

Two important points to note:

  1. Correlation measures linear relationship: not any other relationships. Thus a perfect relationship that is symmetric (y = x^2, for example) will have a correlation coefficient of 0.
  2. Correlation coefficient is a measure of association, not of causality. In the UK, ice cream sales and swimming accidents are correlated. This is not because eating ice cream causes swimming accidents not because people recover from swimming accidents by eating ice cream. In reality, both events are more likely on warm days - such as they are!
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Q: What is correlation coefficient?
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Related questions

Is -0.0001 a correlation coefficient?

Yes it can be a correlation coefficient.


Is 1.5 a correlation coefficient?

No, it cannot be a correlation coefficient.


Is 0.5 the strongest correlation coefficient?

No. The strongest correlation coefficient is +1 (positive correlation) and -1 (negative correlation).


What are the properties of correlation coefficient?

The correlation coefficient is symmetrical with respect to X and Y i.e.The correlation coefficient is the geometric mean of the two regression coefficients. or .The correlation coefficient lies between -1 and 1. i.e. .


What is the correlation coefficient of -2?

A serious error. The maximum magnitude for a correlation coefficient is 1.The Correlation coefficient is lies between -1 to 1 if it is 0 mean there is no correlation between them. Here they are given less than -1 value so it is not a value of correlation coefficient.


What is the feasible range for r the correlation coefficient?

the correlation coefficient range is -1 to +1


What is a Correlation coefficient of 0.00457?

Evidence that there is no correlation.


How is coefficient of determination and coefficient of correlation is related?

coefficient of determination


Is the Correlation Coefficient of 35 strong?

The correlation coefficient must lie between -1 and +1 and so a correlation coefficient of 35 is a strong indication of a calculation error. If you meant 0.35, then it is a weak correlation.


What does a correlation coefficient of zero indicates?

A coefficient of zero means there is no correlation between two variables. A coefficient of -1 indicates strong negative correlation, while +1 suggests strong positive correlation.


What are the properties of correlation?

The correlation coefficient is symmetrical with respect to X and Y i.e.The correlation coefficient is the geometric mean of the two regression coefficients. or .The correlation coefficient lies between -1 and 1. i.e. .


When there is no linear correlation the correlation coefficient equals?

0