The table shows the number of flowers in four bouquets and the total cost of each bouquet. A 2-column table with 4 rows. The first column is labeled number of flowers in the bouquet with entries 8, 12, 6, 20. The second column is labeled total cost in dollars with entries 12, 40, 15, 20. What is the correlation coefficient for the data in the table? –0.57 –0.28 0.28 0.57

Answer:The correct option is;0.28The given data values are;x,      f(x)8,     1212,    406,      1520,    20Where;x = The number of flowers in the bouquetf(x) = The total cost (in dollars) The equation for linear regression is of the form, Y = a + bXThe formula for the intercept, a, and the slope, b, are;\(b = \dfrac{N\sum XY - \le (\sum X \right )\le (\sum Y \right )}{N\sum X^{2} - \le (\sum X \right )^{2}}\)\(a = \dfrac{\sum Y - b\sum X}{N}\)Where:N = 4∑XY = 1066∑X = 46∑Y = 87∑X² = 644(∑X)² = 2116b = (4*1066 - 46*87)/(4*644 - 2116) = 0.5696a = (87 - 0.5696*46)/4 = 15.1996The standard deviation of the x- values \(S_X = \sqrt{\dfrac{\sum (x_i - \mu)^2}{N} }\)\(\sum (x_i - \mu)^2}\) = 115N = 4Sx =√(115/4) Sx = 5.36\(S_Y = \sqrt{\dfrac{\sum (y_i - \mu_y)^2}{N} }\)\(\sum (y_i - \mu_y)^2}\) = 476.75N = 4Sy =√(476.75/4) Sy= 10.92b = r × Sy/Sx Where:r = The correlation coefficientr = b × Sx/Sy = 0.5696*5.36/10.92 = 0.2796 ≈ 0.28The correct option is 0.28.