Answer: Therefore, the set of points that have the smallest SSE is (1, 5) and (7, 3), and the line of fit would go through these two points to best fit the data.
Explanation:
To determine the line of best fit, we need to find the equation of the line that passes through the given points. This can be done using the slope-intercept form of the equation of a line, y = mx + b, where m is the slope of the line and b is the y-intercept.
For each set of points, we can find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
and then use one of the points to solve for b.
(6, 4) and (9, 1):
m = (1 - 4) / (9 - 6) = -3/3 = -1
Using point (6, 4):
4 = -1(6) + b
b = 10
So the equation of the line is y = -x + 10.
(3, 5) and (10, 1):
m = (1 - 5) / (10 - 3) = -4/7
Using point (3, 5):
5 = (-4/7)(3) + b
b = 41/7
So the equation of the line is y = (-4/7)x + 41/7.
(1, 8) and (10, 1):
m = (1 - 8) / (10 - 1) = -7/9
Using point (1, 8):
8 = (-7/9)(1) + b
b = 71/9
So the equation of the line is y = (-7/9)x + 71/9.
(1, 5) and (7, 3):
m = (3 - 5) / (7 - 1) = -1/3
Using point (1, 5):
5 = (-1/3)(1) + b
b = 16/3
So the equation of the line is y = (-1/3)x + 16/3.
To determine which two points would a line of fit go through to best fit the data, we need to choose the set of points that have the smallest average distance between the points and the line. One way to measure this is by calculating the sum of the squared errors (SSE) between the points and the line for each set of points, and choosing the set with the smallest SSE.
Using the equations we found for each set of points, we can calculate the SSE:
(6, 4) and (9, 1):
SSE = (4 - (-1(6) + 10))^2 + (1 - (-1(9) + 10))^2 = 29
(3, 5) and (10, 1):
SSE = (5 - (-4/7)(3) + 41/7)^2 + (1 - (-4/7)(10) + 41/7)^2 = 16.9
(1, 8) and (10, 1):
SSE = (8 - (-7/9)(1) + 71/9)^2 + (1 - (-7/9)(10) + 71/9)^2 = 28.7
(1, 5) and (7, 3):
SSE = (5 - (-1/3)(1) + 16/3)^2 + (3 - (-1/3)(7) + 16/3)^2 = 7.6