To find the correlation coefficient between x and y, we need to first find the standard deviation of x and y.

Standard deviation of x:
The variance of x is given as 9. Therefore, the standard deviation of x is √9 = 3.

Standard deviation of y:
To find the standard deviation of y, we need to first find the sum of squares of residuals (SSR) for both regression lines.

For the first regression line (y=40÷18x):
SSR = Σ(y - ŷ)² = Σ(y - 40÷18x)²
where ŷ is the predicted value of y, given by the regression equation.

Substituting the given values, we get:
SSR = (1-2.22)² + (2-2.78)² + (4-3.33)² + (5-3.89)² + (6-4.44)² + (8-5)²
= 0.52

For the second regression line (x=10÷8y-66÷8):
SSR = Σ(x - ŷ)² = Σ(x - 10÷8y+66÷8)²

Substituting the given values, we get:
SSR = (1-1.37)² + (2-1.97)² + (4-2.86)² + (5-3.46)² + (6-4.06)² + (8-5.25)²
= 6.19

The total sum of squares (SST) for both regression lines can be calculated as follows:

SST = Σ(y - 4)² = (1-4)² + (2-4)² + (4-4)² + (5-4)² + (6-4)² + (8-4)²
= 26

Therefore, the sum of squares of residuals for both regression lines can be used to calculate the coefficient of determination (R²):

R² = 1 - SSR/SST

For the first regression line:
R² = 1 - 0.52/26 = 0.98

For the second regression line:
R² = 1 - 6.19/26 = 0.76

Since R² is a measure of the proportion of variance in y that can be explained by the regression equation, we can see that the first regression line (y=40÷18x) is a better fit for the data. Therefore, we will use this regression equation to estimate y when x=10.

When x=10, y = 40÷18(10) = 22.22

To estimate x when y=10, we can use the same regression equation:

y = 40÷18x
10 = 40÷18x
x = 4.5

Therefore, when y=10, x is estimated to be 4.5.

The correlation coefficient (r) between x and y can be calculated using the formula:

r = Σ((x - x̄)/sx)((y - ȳ)/sy) / (n-1)

where