Calculating the Coefficient of Correlation and Lines of Regression:

Given Data:
x = 1,2,3,4,5,6,7,8,9
y = 2,8,10,12,11,13,14,16,15

Step 1: Find the Mean

- Find the mean of x and y
- Mean of x = sum of x values / total number of x values
- Mean of y = sum of y values / total number of y values

Mean of x = (1+2+3+4+5+6+7+8+9) / 9
Mean of x = 5

Mean of y = (2+8+10+12+11+13+14+16+15) / 9
Mean of y = 11

Step 2: Find the Deviations

- Calculate the deviations of x and y from their respective means
- Deviation of x = x - mean of x
- Deviation of y = y - mean of y

Deviation of x = (1-5), (2-5), (3-5), (4-5), (5-5), (6-5), (7-5), (8-5), (9-5)
Deviation of x = -4, -3, -2, -1, 0, 1, 2, 3, 4

Deviation of y = (2-11), (8-11), (10-11), (12-11), (11-11), (13-11), (14-11), (16-11), (15-11)
Deviation of y = -9, -3, -1, 1, 0, 2, 3, 5, 4

Step 3: Find the Products

- Multiply the deviations of x and y for each observation
- Product = deviation of x * deviation of y

Product = (-4*-9), (-3*-3), (-2*-1), (-1*1), (0*0), (1*2), (2*3), (3*5), (4*4)
Product = 36, 9, 2, -1, 0, 2, 6, 15, 16

Step 4: Find the Summations

- Sum up the deviations of x, deviations of y and products
- Sum of deviation of x = sum of deviation of x values
- Sum of deviation of y = sum of deviation of y values
- Sum of product = sum of product values

Sum of deviation of x = -4-3-2-1+0+1+2+3+4
Sum of deviation of x = 0

Sum of deviation of y = -9-3-1+1+0+2+3+5+4
Sum of deviation of y = 2

Sum of product = 36+9+2-1+0+2+6+15+16
Sum of product = 85

Step 5: Calculate the Coefficient of Correlation

- Use the formula to calculate the coefficient of correlation
- Coefficient of correlation = sum of product / sqrt(sum of deviation of x squared * sum of deviation of y squared)