Contents
What can not be a correlation coefficient?
Understanding the Correlation Coefficient It cannot capture nonlinear relationships between two variables and cannot differentiate between dependent and independent variables. A value of exactly 1.0 means there is a perfect positive relationship between the two variables.
Is 0.47 A strong correlation?
Values between 0.3 and 0.7 (-0.3 and -0.7) indicate a moderate positive (negative) linear relationship via a fuzzy-firm linear rule. Values between 0.7 and 1.0 (-0.7 and -1.0) indicate a strong positive (negative) linear relationship via a firm linear rule.
Is 0.25 a weak correlation?
Similar to Pearson’s r, a value close to 0 means no association. However, a value bigger than 0.25 is named as a very strong relationship for the Cramer’s V (Table 2)….Table 2.
| Phi and Cramer’s V | Interpretation |
|---|---|
| >0.25 | Very strong |
| >0.15 | Strong |
| >0.10 | Moderate |
| >0.05 | Weak |
Can you guess the correlation coefficient of X?
• Correlation coefficient of 0 does not preclude dependence • Can you guess the correlation coefficient of the following functions, where x is a random variable? • Y = 3 * x • Y= 10 * x • Y = 3 * x –1 • Y = x^2 • Y = abs(x) • Y = Sin(x)
Can a correlation coefficient be used for model selection?
The correlation coefficient in question can also be used for model selection: The best model would provide the correlation closest to 1. This is interesting; I am wondering if it is possible to share the data you have adapted for this figure?
Is the coefficient of correlation r ( x, y ) symmetric?
Note that the proposed correlation coefficient R ( X, Y) is not symmetric. One way to get a symmetric version, is to use the maximum between | R ( X, Y) | and | R ( Y, X) |. It will be equal to 1 if and only if there is an exact polynomial or inverse polynomial relationship between X and Y .
How to calculate generalized coefficient of correlation for non-linear relationships?
Use much smoother functions than polnomials, for instance functions that have one extremum (maximum or minimum) at most, and growing not faster than a linear function. Even in that case, use a small number of coefficients in the regression, maybe log (log ( n ))) where n is the number of observations.