the coefficient correlation between two variable is 0.5 then the coeff...
Explanation of Coefficient of Correlation and Determination
What is Coefficient of Correlation?
The coefficient of correlation is a measure of the strength of the relationship between two variables. It is a numerical value between -1 and 1. A value of -1 indicates a perfect negative correlation, a value of 0 indicates no correlation, and a value of 1 indicates a perfect positive correlation.
What is Coefficient of Determination?
The coefficient of determination is a measure of the proportion of the variance in one variable that is predictable from the other variable. It is a value between 0 and 1. A value of 0 indicates that none of the variance in one variable is predictable from the other variable, and a value of 1 indicates that all of the variance in one variable is predictable from the other variable.
Relationship between Coefficient of Correlation and Determination
The coefficient of determination is equal to the square of the coefficient of correlation. Therefore, if the coefficient of correlation between two variables is 0.5, the coefficient of determination is 0.25 (0.5 squared). This means that 25% of the variance in one variable is predictable from the other variable.
Conclusion
In conclusion, the coefficient of correlation and determination are both measures of the relationship between two variables. The coefficient of correlation measures the strength of the relationship, while the coefficient of determination measures the proportion of the variance that is predictable. The coefficient of determination is equal to the square of the coefficient of correlation.