Solution:

Given data:

x: 2 3 5 4 7

y: 4 6 7 8 10

Coefficient of Correlation (r) = 0.93

We need to find the correlation between u and v.

Steps to find the correlation between u and v:

Step 1: Find the mean of u and v.

Step 2: Find the standard deviation of u and v.

Step 3: Find the deviation of u and v from their respective means.

Step 4: Multiply the deviations of u and v.

Step 5: Add all the products obtained in Step 4.

Step 6: Divide the result obtained in Step 5 by the product of the standard deviation of u and v.

Step 7: The result obtained in Step 6 is the correlation between u and v.

Calculation:

The mean of u and v can be calculated as follows:

Mean of u = (-3 - 2 + 0 - 1 + 2)/5 = -0.8

Mean of v = (-4 - 2 - 1 + 0 + 2)/5 = -1

The standard deviation of u and v can be calculated as follows:

Standard deviation of u = √[(-3 - (-0.8))^2 + (-2 - (-0.8))^2 + (0 - (-0.8))^2 + (-1 - (-0.8))^2 + (2 - (-0.8))^2]/5

= √[29.36]/5 = 1.716

Standard deviation of v = √[(-4 - (-1))^2 + (-2 - (-1))^2 + (-1 - (-1))^2 + (0 - (-1))^2 + (2 - (-1))^2]/5

= √[18]/5 = 0.9487

The deviations of u and v from their respective means can be calculated as follows:

Deviation of u = u - Mean of u

= -3 - (-0.8) , -2 - (-0.8) , 0 - (-0.8) , -1 - (-0.8) , 2 - (-0.8)

= -2.2 , -1.2 , 0.8 , -0.2 , 2.8

Deviation of v = v - Mean of v

= -4 - (-1) , -2 - (-1) , -1 - (-1) , 0 - (-1) , 2 - (-1)

= -3 , -1 , 0 , 1 , 3

The products of deviations of u and v can be calculated as follows:

Product of deviations = (-2.2) × (-3) + (-1.2) × (-1) + 0.8 × 0 + (-0.2) × 1 + 2.8 × 3

= -6.6 + 1.2 + 8.4 - 0.2 + 8.4

= 11.2

The correlation between u and v can be calculated as follows:

Correlation between u and v = Product of deviations/(Standard deviation of u × Standard deviation of v)

= 11.2/(1.