To find the correlation coefficient of the data, we can use the formula for Pearson's correlation coefficient:
r = [Σ((X_i - X̄)(Y_i - Ȳ))] / [√(Σ(X_i - X̄)^2) * √(Σ(Y_i - Ȳ)^2)]
First, we need to calculate the means of the temperature and number of ice cream cones sold:
X̄ (mean temperature) = (82 + 85 + 89 + 91 + 92 + 84 + 82 + 78) / 8 = 85.375
Ȳ (mean ice cream cones sold) = (110 + 120 + 130 + 135 + 135 + 120 + 115 + 105) / 8 = 121.25
Next, we calculate the deviations from the mean for temperature (X) and ice cream cones sold (Y), as well as the products of these deviations:
X_i - X̄:
-3.375, -0.375, 3.625, 5.625, 6.625, -1.375, -3.375, -7.375
Y_i - Ȳ:
-11.25, -1.25, 8.75, 13.75, 13.75, -1.25, -6.25, -16.25
(X_i - X̄)(Y_i - Ȳ):
38.016, 0.469, 31.844, 77.344, 91.094, 1.719, 21.094, 119.844
Now, we sum up these values to calculate the correlation coefficient:
Σ((X_i - X̄)(Y_i - Ȳ)) = 200.424
Next, we calculate the sums of squares for X and Y:
Σ(X_i - X̄)^2 = 82.78125
Σ(Y_i - Ȳ)^2 = 1610
Now, we calculate the correlation coefficient:
r = 200.424 / √(82.78125 * 1610) ≈ 0.508
Therefore, the correlation coefficient of the set of data is approximately 0.508. So, the answer is:
4) 0.508
The table shows the temperature (in degrees) for eight consecutive days as well as the respective number of ice cream cones an ice cream shop sold on each of these days.
What is the correlation coefficient of the set of data? Round your answer to the nearest thousandth.
1) 0.956
2) 0.019
3) -0.0972
4) 0.508
1 answer