Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 1 - Section 1.4 - Linear Regression - Exercises - Page 102: 15

Answer

\begin{array}{|c|c|c|c|c|} \hline & x & y & xy & xx \\ \hline & 2 & 0 & 0 & 4 \\ & 6 & 70 & 420 & 36 \\ & 10 & 900 & 9000 & 100 \\\hline \Sigma & {\bf 18} & {\bf 970} & {\bf 9420} & {\bf 140} \\\hline \end{array} $y=112.5x-351.7$ $998.3$ million in 2012

Work Step by Step

Regression line: $y=mx+b,$ $m=\displaystyle \frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}\qquad b=\frac{\sum y-m(\sum x)}{n}$ $n=$ number of data points. ----- \begin{array}{|c|c|c|c|c|} \hline & x & y & xy & xx \\ \hline & 2 & 0 & 0 & 4 \\ & 6 & 70 & 420 & 36 \\ & 10 & 900 & 9000 & 100 \\\hline Sigma & {\bf 18} & {\bf 970} & {\bf 9420} & {\bf 140} \\\hline \end{array} $m=\displaystyle \frac{3(9420)-(10)(970)}{n(140)-(18)^{2}}=112.5$ $b=\displaystyle \frac{970-112.5(18)}{3}=-351.7$ $y=112.5x-351.7$ In 2012, x=12 and $y=112.5(12)-351.7=998.3$
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