Question

Arrange the following steps of calculating partial and multiple correlation co-efficient for a 3-variable problem from start to end:
A. Computing partial $\sigma$'s.
B. Writing the regression equations.
C. Computing of partial regression co-efficients.
D. Computing the partial $r$'s.
E. Computation of multiple correlation co-efficient, R.
Choose the correct answer from the options given below:

• A. D - B - C - A - E
• B. B - D - A - C - E
• C. A - C - D - E - B
• D. C - A - E - D - B

Hint:

In multiple correlation calculations, setting up the basic regression equations (B) is always the starting step, and the final combined multiple correlation coefficient ($R$) is always the last output value calculated (E).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks us to identify the correct step-by-step mathematical sequence for calculating partial and multiple correlation coefficients in a three-variable statistics problem.

Step 2: Detailed Explanation:

• In multivariate statistical analysis, calculating the relationships between three variables follows a structured mathematical order:

• B. Writing the regression equations: The first step requires defining the relationships between the three variables by setting up the linear regression equations.

• D. Computing the partial $r$'s: Next, we calculate the zero-order and first-order partial correlation coefficients ($r$) to establish basic correlations.

• A. Computing partial $\sigma$'s: We then calculate the standard errors of estimate and partial standard deviations ($\sigma$) for the residuals of the variables.

• C. Computing of partial regression co-efficients: These values are used to calculate the partial regression coefficients ($b$ weights).

• E. Computation of multiple correlation co-efficient, R: Finally, using the calculated partial coefficients, we compute the overall multiple correlation coefficient ($R$), which represents the combined predictive power of the independent variables.

• This standard statistical procedure corresponds to the sequence: B $\rightarrow$ D $\rightarrow$ A $\rightarrow$ C $\rightarrow$ E.

Step 3: Final Answer:
The correct step-by-step sequence for calculating these correlation coefficients is B - D - A - C - E.