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
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What do you mean by measures of central tendency? Also find the missing frequency for the following frequency distribution if median is given 25:
Write the properties Of a good measure Of dispersion. The following information for the two groups of individuals is given as:
If each value of X is multiplied by 10 and each value of Y is multiplied by 20, then the modified regression coefficient 
would be the half of previous.
Calculate the first, second and third quartile for following data:
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 05 | 15 | 30 | 12 | 08 |
Why are two different lines of regression used to obtain the optimum values of two
variables X and Y. The marks of lo students of a class in Mathematics and Statistics are given below:
| Marks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Mathematics | 40 | 46 | 42 | 30 | 35 | 28 | 39 | 43 | 25 | 45 |
| Statistics | 35 | 41 | 36 | 32 | 42 | 48 | 29 | 38 | 28 | 40 |
The sum of deviations of 15 value from their main is 15.
