Question

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 1

C on edge

Explanation:

Answer 2

The correct option is;

0.28

Explanation:

The given data values are;

x, f(x)

8, 12

12, 40

6, 15

20, 20

Where;

x = The number of flowers in the bouquet

f(x) = The total cost (in dollars)

The equation for linear regression is of the form, Y = a + bX

The formula for the intercept, a, and the slope, b, are;

`b = (N\sum XY - \left (\sum X \right )\left (\sum Y \right ))/(N\sum X^(2) - \left (\sum X \right )^(2))`

`a = (\sum Y - b\sum X)/(N)`

Where:

N = 4

∑XY = 1066

∑X = 46

∑Y = 87

∑X² = 644

(∑X)² = 2116

b = (4*1066 - 46*87)/(4*644 - 2116) = 0.5696

a = (87 - 0.5696*46)/4 = 15.1996

The standard deviation of the x- values

`S_X = \sqrt{(\sum (x_i - \mu)^2)/(N) }`

`\sum (x_i - \mu)^2}` = 115

N = 4

Sx =√(115/4)

Sx = 5.36

`S_Y = \sqrt{(\sum (y_i - \mu_y)^2)/(N) }`

`\sum (y_i - \mu_y)^2}` = 476.75

N = 4

Sy =√(476.75/4)

Sy= 10.92

b = r × Sy/Sx

Where:

r = The correlation coefficient

r = b × Sx/Sy = 0.5696*5.36/10.92 = 0.2796 ≈ 0.28

The correct option is 0.28.