Question

The table shown below gives the national average pupil-teacher ratio in public schools over selected years.

\begin{array}{|c|c|}
\hline \text { Year } & \text { Ratio } \\
\hline 1992 & 19.4 \\
\hline 1996 & 19.7 \\
\hline 2000 & 18.9 \\
\hline 2004 & 18.2 \\
\hline 2008 & 16.8 \\
\hline
\end{array}

Find the equation for the least squares line. Let \(x\) correspond to the number of years since 1992 and let \(y\) correspond to the average number of pupils per 1 teacher.

Answer 1

Enter the data into Desmos (desmos.com), You should end up with a screen like the one below.

Take special note of the data values in the first column. The \(x\) values (in this case called \(x_{1}\) ) are described as the number of years since \(1992 .\) This means that \(1992,1996,2000, \ldots\) corresponds to 0 , \(4,8, \ldots\)

Examining the screen above, we see that \(m=-0.1675\) and \(b=19.94\). This means the equation of the least squares line is
\[
y=-0.1675 x+19.94
\]