The Linear Correlation Coefficient Calculation

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.
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