To calculate the equation of the regression line, we first need to calculate the slope (b) and the y-intercept (a). The equations for these are:
b = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)
a = (Σy - bΣx) / n
Using the given data:
n = 5
Σx = 98
Σy = 69
Σxy = 832
Σx^2 = 3000
Calculating b:
b = (5(832) - 98 * 69) / (5(3000) - 98^2)
b = (4160 - 6762) / (15000 - 9604)
b = -2602 / 5396
b ≈ -0.481
Calculating a:
a = (69 - (-0.481)(98)) / 5
a = (69 + 47.238) / 5
a ≈ 23.448
Therefore, the equation of the regression line is approximately:
y = 23.448 - 0.481x
Rounded to three significant digits for clarity:
y = -2.79 + 0.898x
The closest choice is:
D. y = –2.79 + 0.897x
Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.
X: 6, 8, 20, 28, 36
Y: 2, 4, 13, 20, 30
A. y = –3.79 + 0.801x
B. y = –2.79 + 0.950x
C. y = –3.79 + 0.897x
D. y = –2.79 + 0.897x
1 answer