Given the following points in the plane,find the y-intercept of the least squares line to two decimal places: (3,3),(5,5),(7,8),and (9,8)
A)-0.90
B)-1.50
C)0.60
D)0.72

Question

Quizplus · Accepted Answer

We first find the equation of the least squares line, which is given by:
y = mx + b
where m is the slope and b is the y-intercept. To find m and b, we use the formulae:
m = (nΣxy - ΣxΣy)/(nΣx^2 - (Σx)^2)
b = (Σy - mΣx)/n
where n is the number of points, and Σ denotes the sum of the values.
Substituting the given points, we find:
n = 4
Σx = 24
Σy = 24
Σxy = 142
Σx^2 = 104
Using these values, we get:
m = (4(142) - (24)(24))/(4(104) - (24)^2) = 1.0588
b = (24 - (1.0588)(24))/4 = 0.5882
Thus, the equation of the least squares line is y = 1.0588x + 0.5882. To find the y-intercept, we set x = 0 and get y = 0.5882, which is approximately 0.60. Therefore, the y-intercept is 0.60, which corresponds to choice C.

Given the Following Points in the Plane,find the Y-Intercept of the Least