Calculating the Coefficient of Correlation

To calculate the coefficient of correlation from the given data, we need to follow the steps below:

Step 1: Find the mean of both x and y values.
- Mean of x (x̄) = (1+2+3+4+5)/5 = 3
- Mean of y (ȳ) = (8+6+7+5+5)/5 = 6.2

Step 2: Calculate the deviations of x and y from their respective means.
- Deviation of x (dx) = x - x̄
- Deviation of y (dy) = y - ȳ
- dx: -2 -1 0 1 2
- dy: 1 -0.2 0.8 -1.2 -1.2

Step 3: Calculate the product of deviations for each pair of x and y values.
- Product of deviations (dx*dy): -2*1 = -2, -1*(-0.2) = 0.2, 0*0.8 = 0, 1*(-1.2) = -1.2, 2*(-1.2) = -2.4

Step 4: Calculate the sum of all the products of deviations.
- Sum of (dx*dy) = -2 + 0.2 + 0 - 1.2 - 2.4 = -5.4

Step 5: Calculate the standard deviation of x and y values.
- Standard deviation of x (σx) = √[Σ(x - x̄)²/n]
- σx = √[((1-3)² + (2-3)² + (3-3)² + (4-3)² + (5-3)²)/5] = 1.414
- Standard deviation of y (σy) = √[Σ(y - ȳ)²/n]
- σy = √[((8-6.2)² + (6-6.2)² + (7-6.2)² + (5-6.2)² + (5-6.2)²)/5] = 1.166

Step 6: Calculate the coefficient of correlation using the formula.
- Coefficient of correlation (r) = Σ(dx*dy)/[σx*σy*(n-1)]
- r = -5.4/[1.414*1.166*(5-1)] = -0.559

Therefore, the coefficient of correlation from the given data is -0.559. It indicates a moderately negative correlation between the x and y values.

-0.85