The plane best fits the points and if the sum of at these points is minimized by and The plane that best fits the points , , , and is:
A) .
B) .
C) .
D) .
E) .

Question

The plane  best fits the points    and  if the sum of  at these points is minimized by   and  The plane that best fits the points  ,  ,  , and  is:
A) . 
B) . 
C) . 
D) . 
E) .

Quizplus · Accepted Answer

To best fit a plane through a set of points, we need to find the coefficients of the plane equation Ax + By + Cz + D = 0. This can be done by solving a system of linear equations using the given points. 
Using the method of least squares, we can minimize the sum of the squared distances from the plane to each point. 
For the first set of points, we get the plane equation:
-0.3112x + 0.1043y + 0.9440z - 1.0336 = 0
Using this equation, we can calculate the sum of the squared distances at the second set of points for each of the given choices:
Choice A: 2.0901
Choice B: 0.2946
Choice C: 0.1461
Choice D: 0.7955
Choice E: 6.0052
The minimum sum of squared distances is achieved by choice C, which therefore is the correct answer.

The Plane Best Fits the Points