Question

Suppose we use least-squares approach to find the line $f(x) = a + bx$ that best fits the points \begin{tabular}{c|c|c|c|c|c|c|c} $x_k$ & $-2$ & $0$ & $2$ & $4$ & $1$ & $-4$ & $-3$ & $3$ \\ $y_k$ & $-3$ & $1$ & $1$ & $3$ & $-1$ & $-3$ & $-1$ & $0$ \\ \end{tabular} (a) Find explicitly the system of linear equations $2 \times 2$ that can be used to solve for $a$ and $b$. (b) Use Matlab/Julia to solve the system and sketch the line.

          Suppose we use least-squares approach to find the line $f(x) = a + bx$ that best fits the points
\begin{tabular}{c|c|c|c|c|c|c|c}
$x_k$ & $-2$ & $0$ & $2$ & $4$ & $1$ & $-4$ & $-3$ & $3$ \\ 
$y_k$ & $-3$ & $1$ & $1$ & $3$ & $-1$ & $-3$ & $-1$ & $0$ \\
\end{tabular}
(a) Find explicitly the system of linear equations $2 \times 2$ that can be used to solve for $a$ and $b$.
(b) Use Matlab/Julia to solve the system and sketch the line.

Suppose we use least-squares approach to find the line f(x) = a + bx that best fits the points

xk -2 0 2 4 1 -4 -3 3

yk -3 1 1 3 -1 -3 -1 0

(a) Find explicitly the system of linear equations 2 × 2 that can be used to solve for a and b.
(b) Use Matlab/Julia to solve the system and sketch the line.

Added by Patrick V.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

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Solved by Expert John Incabo

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Suppose we use the least-squares approach to find the line f = a + bx that best fits the points (-20, 241), (-3, 113), and (11, -3). (a) Find explicitly the system of linear equations that can be used to solve for a and b. (b) Use Matlab/Julia to solve the system and sketch the line.