Correlation Strength and Common Variance
The strength of a relationship indicated by a correlation coefficient ($r$) is determined by its absolute value, $|r|$. Common variance, which represents the proportion of variance shared between two variables, is proportional to the square of the correlation coefficient, $r^2$. Therefore, a higher absolute value of $r$ signifies a stronger relationship and greater common variance.
Ranking Correlation Coefficients
To arrange the given correlation coefficients in descending order of strength, we compare their absolute values:
- The correlation coefficients are: $-0.8$, $0.7$, $-0.5$, $0.4$.
- Calculate the absolute value for each:
- $|-0.8| = 0.8$
- $|0.7| = 0.7$
- $|-0.5| = 0.5$
- $|0.4| = 0.4$
- Arrange these absolute values in descending order: $0.8$, $0.7$, $0.5$, $0.4$.
- The corresponding original correlation coefficients in descending order of strength are: $-0.8$, $0.7$, $-0.5$, $0.4$.
Final Ordering
The correlation coefficients arranged in descending order of their strength (based on common variance) are: $-0.8$, $0.7$, $-0.5$, $0.4$. This matches Option A.
Important Questions from Correlation Analysis
The value of simple correlation coefficient lies in the interval:
Which option is correct for the correlation ratio E 2?
Let θ be the angle made by the line of regression of Y on X. If σ Y= 2σ X and the correlation coefficient between X and Y is 0.3, the value θ equals
The multiple correlation coefficient R 1,23 as compared to any simple correlation coefficients between the distinct variable X 1 ,X 2, and X 3is
The coefficients of the regression β X|y and β Y|x , are known, The coefficient of correlation equals:
