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Mathematics-Online problems:

Interactive Problem 277: Determination of Best Fitting Plane

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Determine the plane

$\displaystyle E: \quad z=p(x,y)=ax+by+c $

defined by
$ x_{i}$ 1 3 2 5
$ y_{i}$ $ -4$ $ -2$ 0 4
$ z_{i}$ 0 $ -2$ 2 0
for which the sum over the squares of the offsets $ \vert z_{i}-p(x_{i},y_{i})\vert^{2}$ is minimal.

Determine the parameters in such a way that $ E$ includes the line

$\displaystyle g:\ \ \left(\begin{array}{c}2 \\ 1\\ 0\end{array}\right) +t\left(\begin{array}{c}1 \\ 1\\ 1\end{array}\right)\,, \qquad t\in\mathbb{R}\, . $


Solution: Round the results off to four decimal places.

Parameters of the best fitting plane $ E$:
$ a=$, $ b=$, $ c=$.

Parameters of the best fitting plane, including $ g$ :
$ a=$, $ b=$, $ c=$.


   

(Authors: Höllig/Höfert)

see also:

  automatically generated: 3/12/2018