Derive the formula for the coefficient of partial correlation coefficient R1.23, R2.13 and R3.12 for the following data:
| X1 | 10 | 20 | 30 | 40 | 50 |
| X2 | 20 | 30 | 40 | 50 | 60 |
| X3 | 30 | 40 | 50 | 60 | 70 |
To calculate the coefficient of partial correlation (R) between three variables, X1, X2, and X3, while controlling for the effect of the other variables, you can use the following formula for R1.23 (the partial correlation between X1 and X3 while controlling for X2):
\[ R1.23 = \frac{r_{13} - r_{12} \cdot r_{23}}{\sqrt{(1 - r_{12}^2)(1 - r_{23}^2)}} \]
Where:
- \( r_{13} \) is the correlation coefficient between X1 and X3.
- \( r_{12} \) is the correlation coefficient between X1 and X2.
- \( r_{23} \) is the correlation coefficient between X2 and X3.
Before we can use this formula, we need to calculate the correlation coefficients for the pairs of variables. Let's calculate these values step by
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Derive the formula for the coefficient of partial correlation coefficient R1.23, R2.13 and R3.12 for the following data:
| X1 | 10 | 20 | 30 | 40 | 50 |
| X2 | 20 | 30 | 40 | 50 | 60 |
| X3 | 30 | 40 | 50 | 60 | 70 |
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| Frequency | 05 | 15 | 30 | 12 | 08 |
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