I have calculated the Pearson correlation coefficient for two sets of values using excel. I got the value in the negative number. I know that the idea of getting a negative correlation means that the two variables are reversely proportional. Now, I have to calculate multiple/joint correlation between other variables. The idea of the multiple correlation is explained here: https://www.real-statistics.com/correlation/multiple-correlation/
Should I use only the absolute value of the first correlation for that case? Or should I use the exact value with the sign? Please guide.
I am not sure what you mean by "multiple/joint correlation" but if you are talking about indirect effects (mediation), you need to maintain the sign of the correlation.
I think you can use the absolute value if the aim to respond to the direction of the relationship.
I think you can use the absolute value if the aim to respond to the direction of the relationship.
Multiple correlation is explained here: https://www.real-statistics.com/correlation/multiple-correlation/
I want to use individual correlation values to compute this multiple correlation. I get two different results with using the sign or without using the sign for all values. Which is the correct one?
Lahari, what you're referring to multiple correlation is mediation (as explained in the link you shared with us).
To calculate this multiple correlation (mediation) you will have to keep the sign. Otherwise, you'll have wrong coefficients in the multiple correlation.
Always use the sign with the Pearson correlation coefficient. ["...the *direction* of the relationship" *requires* a sign.]
As per people's recommendation, I used the sign in my calculation. But, sometimes I am skeptical about the result. An example is:
1. Individual correlation between variable A and variable H is 0.46
2. Individual correlation between variable B and H is 0.22
3. Correlation between A and B is -0.63
Now, the joint correlation of A and B to H is (using sign):
= SQRT((0.46^2 + 0.22^2 - 2*0.46*0.22*(-0.63)) / (1-(-0.63)^2)) = SQRT((0.21 + 0.05 + 0.13) / 0.60) = SQRT(0.65)
= 0.8
Now, the joint correlation of A and B to H is (without using sign):
= SQRT((0.46^2 + 0.22^2 - 2*0.46*0.22*0.63) / (1-0.63^2)) = SQRT((0.21 + 0.05 - 0.13) / 0.60) = SQRT(0.21)
= 0.46
Here, it seems 0.8 is a very high correlation, whether, 0.46 seems realistic. What is your understanding? Wayne Fischer Ali Farooq David L Morgan
Sorry, Lahari...what is the *physical* meaning of a joint *correlation* amongst three variables?
As per my understanding, the joint correlation amongst three variables signifies how much the measuring variable is linearly related to the combination of two known variables.
I agree with Wayne, Lahari, you should always "use the sign with the Pearson correlation coefficient". BTW, this is exactly the idea of this coefficient, to show both, the strength and the direction of the relationship between the variables.
About your last comment. Multiple r is difficult to interpret directly in terms of individual/joint relationships because it's a complex measure which involves more than two dimensions! So, .8 could be real. My recommendation is to use statistical software (even Excel in regression provides multiple r).
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