What is the linear correlation coefficient between the ages and annual pharmacy bills of 9 randomly selected employees?
Final answer: 0.960
Calculation of Linear Correlation Coefficient
Linear correlation coefficient (r) formula:
r = Σ[(x - x̄)(y - ȳ)] / √[Σ(x - x̄)² * Σ(y - ȳ)²]
Where:
x̄ = mean of ages
ȳ = mean of pharmacy bills
Σ = sum of
x = age values
y = pharmacy bill values
First, we need to find the mean of ages (x) and mean of pharmacy bills (y).
x̄ = (40 + 43 + 47 + 50 + 53 + 55 + 59 + 63 + 67) / 9 = 53.33
ȳ = (111 + 115 + 118 + 126 + 137 + 140 + 143 + 145 + 147) / 9 = 133.33
Next, we calculate the deviations of each data point from the mean:
x deviations: (-13.33, -10.33, -6.33, -3.33, -0.33, 1.67, 5.67, 9.67, 13.67)
y deviations: (-22.33, -18.33, -15.33, -7.33, 3.67, 6.67, 9.67, 11.67, 13.67)
Then, we multiply the deviations together to find the sum of the products:
Σ[(x - x̄)(y - ȳ)] = 679.33
Next, we find the sum of the squares of the deviations for both x and y:
Σ(x - x̄)² = 245.33
Σ(y - ȳ)² = 424.33
Finally, we calculate the linear correlation coefficient:
r = 679.33 / √(245.33 * 424.33) = 0.960
Therefore, the linear correlation coefficient between the ages and annual pharmacy bills of the 9 employees is 0.960.