If r and R denote correlation and multiple correlation coefficient for the data set for X₁, X₂ and X₃. Which option is correct?

Question

Question

This question was previously asked in

SSC CGL Tier-II ( JSO ) 2021 Official Paper ( Held On: 10 August 2022 )

Answer 1

The correct answer is r_12=0.69,r_13=0.22,r_23=0.23,R_1.23=.69

Key Points

Correlation coefficient (r) measures the linear association between two variables.
Multiple correlation coefficient (R) measures the strength of the association between multiple predictor variables and a single criterion variable.
The values of r and R range between -1 and 1.
Values close to 1 indicate a strong positive association (or relationship), values close to -1 indicate a strong negative association (or relationship), and values close to 0 indicate no or weak association (or relationship).
Correlation coefficients (r) and multiple correlation coefficients (R) are useful for understanding the relationships between variables in a data set.

Additional Information

If r12 represents the correlation between X1 and X2, r13 represents the correlation between X1 and X3, and r23 represents the correlation between X2 and X3, then the values of r12, r13, and r23 should range between -1 and 1, with values close to 1 indicating a strong positive association, values close to -1 indicating a strong negative association, and values close to 0 indicating no or weak association.
The multiple correlation coefficient (R) measures the strength of the association between multiple predictor variables (X1, X2, X3) and a single criterion variable.
In this case, R1.23 represents the multiple correlation between X1, X2, and X3 with respect to the criterion variable.
Like r, R values range between -1 and 1, with values close to 1 indicating a strong relationship and values close to 0 indicating a weak relationship.
So, based on the given values, r12=0.69, r13=0.22, r23=0.23, R1.23=.69

Important Points

It is important to note that correlation does not imply causation, meaning that just because two variables are correlated does not mean that one causes the other.
Correlation and multiple correlation coefficients are based on linear relationships and may not capture non-linear relationships between variables.
Interpreting the strength and direction of relationships between variables is an important aspect of data analysis and interpretation.