What is the correlation coefficient of the equation?

X 3.0, 7.3, 4.5, 3.3, 7.6
Y 9.8, 8.3, 8.6, 9.8, 8.8

To find the correlation coefficient, we first need to calculate the means of X and Y:

Mean of X (X̄) = (3.0 + 7.3 + 4.5 + 3.3 + 7.6) / 5 = 25.7 / 5 = 5.14
Mean of Y (Ȳ) = (9.8 + 8.3 + 8.6 + 9.8 + 8.8) / 5 = 45.3 / 5 = 9.06

Next, we calculate the numerator of the correlation coefficient formula:

Σ[(X - X̄)(Y - Ȳ)] = (3.0 - 5.14)(9.8 - 9.06) + (7.3 - 5.14)(8.3 - 9.06) + (4.5 - 5.14)(8.6 - 9.06) + (3.3 - 5.14)(9.8 - 9.06) + (7.6 - 5.14)(8.8 - 9.06)
= (-2.14)(0.74) + (2.16)(-0.76) + (-0.64)(-0.46) + (-1.84)(0.74) + (2.46)(-0.26)
= -1.5816 - 1.6416 + 0.2944 - 1.3616 - 0.6396
= -5.93

Next, we calculate the denominator of the correlation coefficient formula:

√[Σ(X - X̄)^2 * Σ(Y - Ȳ)^2] = √[(1.8824)(1.73) * (0.6724)(14.13)] = √[3.2569 * 9.5222] = √30.9836 ≈ 5.56

Finally, we calculate the correlation coefficient:

r = Σ[(X - X̄)(Y - Ȳ)] / [√Σ(X - X̄)^2 * Σ(Y - Ȳ)^2] = -5.93 / 5.56 ≈ -1.064

Therefore, the correlation coefficient of the given data is approximately -1.064.