Linear Regression

Multiple Regression calculates linear-regression equations with keyed or labeled data matrices. The result is an equation expressing the variable at the head of the first column as a linear combination of the variables heading the remaining columns, plus a constant (that is missing if Multiple Regression (no constant) was chosen). The equation produced is the best fit to the data in the least-squares sense.

$\blacktriangleright$ Statistics + Fit Curve to Data + Multiple Regression

$\left[\vphantom{
\begin{array}{cc}
y & x \\
0\;\; & 1.1 \\
0.5 & 1.5 \\
1\;\; & 1.9 \\
1.5 & 2.4 \\
2\;\; & 2.9
\end{array}
}\right.$$\begin{array}{cc}
y & x \\
0\;\; & 1.1 \\
0.5 & 1.5 \\
1\;\; & 1.9 \\
1.5 & 2.4 \\
2\;\; & 2.9
\end{array}$$\left.\vphantom{
\begin{array}{cc}
y & x \\
0\;\; & 1.1 \\
0.5 & 1.5 \\
1\;\; & 1.9 \\
1.5 & 2.4 \\
2\;\; & 2.9
\end{array}
}\right]$, Regression is: y = - 1.1703 + 1.1073x


$\left(\vphantom{
\begin{array}{cc}
x & y \\
a & b \\
c & d
\end{array}
}\right.$$\begin{array}{cc}
x & y \\
a & b \\
c & d
\end{array}$$\left.\vphantom{
\begin{array}{cc}
x & y \\
a & b \\
c & d
\end{array}
}\right)$, Regression is: x = ${\dfrac{{ad-bc}}{{d-b}}}$ - ${\dfrac{{a-c}}{{d-b}}}$y 

$\blacktriangleright$ Statistics + Fit Curve to Data + Multiple Regression

$\left[\vphantom{
\begin{array}{ccc}
z & x & y \\
1 & 0\;\; & 1.1 \\
2 ...
... & 1\;\; & 1.9 \\
5 & 1.5 & 1.9 \\
7 & 2\;\; & 2.9
\end{array}
}\right.$$\begin{array}{ccc}
z & x & y \\
1 & 0\;\; & 1.1 \\
2 & 0.5 & 1.1 \\
4 & 1\;\; & 1.9 \\
5 & 1.5 & 1.9 \\
7 & 2\;\; & 2.9
\end{array}$$\left.\vphantom{
\begin{array}{ccc}
z & x & y \\
1 & 0\;\; & 1.1 \\
2 ...
... & 1\;\; & 1.9 \\
5 & 1.5 & 1.9 \\
7 & 2\;\; & 2.9
\end{array}
}\right]$, Regression is: z = - .126 + 2.09x + 1.03y

The choice Multiple Regression (no constant) gives the following linear equations.

$\blacktriangleright$ Statistics + Fit Curve to Data + Multiple Regression (no constant)

$\left[\vphantom{
\begin{array}{cc}
u & v \\
0\;\; & 1.1 \\
0.5 & 1.5 \\
1\;\; & 1.9 \\
1.5 & 2.4 \\
2\;\; & 2.9
\end{array}
}\right.$$\begin{array}{cc}
u & v \\
0\;\; & 1.1 \\
0.5 & 1.5 \\
1\;\; & 1.9 \\
1.5 & 2.4 \\
2\;\; & 2.9
\end{array}$$\left.\vphantom{
\begin{array}{cc}
u & v \\
0\;\; & 1.1 \\
0.5 & 1.5 \\
1\;\; & 1.9 \\
1.5 & 2.4 \\
2\;\; & 2.9
\end{array}
}\right]$, Regression is: u = .56733v


$\left[\vphantom{
\begin{array}{ccc}
z & x & y \\
1 & 0\;\; & 1.1 \\
2 ...
... & 1\;\; & 1.9 \\
5 & 1.5 & 1.9 \\
7 & 2\;\; & 2.9
\end{array}
}\right.$$\begin{array}{ccc}
z & x & y \\
1 & 0\;\; & 1.1 \\
2 & 0.5 & 1.1 \\
4 & 1\;\; & 1.9 \\
5 & 1.5 & 1.9 \\
7 & 2\;\; & 2.9
\end{array}$$\left.\vphantom{
\begin{array}{ccc}
z & x & y \\
1 & 0\;\; & 1.1 \\
2 ...
... & 1\;\; & 1.9 \\
5 & 1.5 & 1.9 \\
7 & 2\;\; & 2.9
\end{array}
}\right]$, Regression is: z = 2.1829x + .91245y


$\left(\vphantom{
\begin{array}{cc}
x & y \\
a & b \\
c & d
\end{array}
}\right.$$\begin{array}{cc}
x & y \\
a & b \\
c & d
\end{array}$$\left.\vphantom{
\begin{array}{cc}
x & y \\
a & b \\
c & d
\end{array}
}\right)$, Regression is: x = ${\dfrac{{ba+dc}}{{b^{2}+d^{2}}}}$y