# The following table lists the annual amounts of glass cullet produced by Kimble Glass Works, Inc. Year Code Scrap (tons) 1999 1 2.0 2000 2 4.0 2001 3 3.0 2002 4 5.0 2003 5 6.0 Determine the least squares trend equation. Estimate the amount of scrap for the year 2005.

The following table lists the annual amounts of glass cullet produced by Kimble Glass Works, Inc.

$$\begin {array}{|c|c|} \hline \text{Year}&\text{Code}&\text{Scrap (tons)}\\ \hline 1999&1&2.0\\ \hline 2000&2&4.0\\ \hline 2001&3&3.0\\ \hline 2002&4&5.0\\ \hline 2003&5&6.0\\ \hline \end {array}$$

Determine the least squares trend equation. Estimate the amount of scrap for the year 2005.

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Nathaniel Kramer

First we have to draw a graph by then we can observethat this graph shows a straight line. So we have tofit a strainght line
Y= a+bX
where y is the scrap in tons and X is the years, take years as 1, 2, 3, 4, and 5 then
$$\begin{matrix}12&1&12&1\\24&2&48&4\\33&3&99&9\\45&4&180&16\\56&5&280&25\end{matrix}$$
total
$$\begin{matrix}170&15&619&55\end{matrix}$$
we know that the normal equations for straight line are