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 103: 19

Answer

$y=0.135p+0.15$ Jobs created at $ 50\%$ recovery level: about $7.$

Work Step by Step

The regression line is $\qquad y=mx+b$, where $m$ and $b$ are computed as follows. $m=\displaystyle \frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}\qquad b=\frac{\sum y-m(\sum x)}{n},$ $n=$ number of data points. $\left[\begin{array}{lllll} & p & y & py & p^{2}\\ & & & & \\ \hline & 20 & 3 & 60 & 400\\ & 40 & 6 & 240 & 1600\\ & 80 & 9 & 720 & 6400\\ & 100 & 15 & 1500 & 10,000\\ \hline & & & & \\ \sum & 240 & 33 & 2520 & 18,400\\ & & & & \end{array}\right]$ $m=\displaystyle \frac{4(2520)-(240)(33)}{4(18,400)-(240)^{2}}=\frac{27}{200}=0.135$ $b=\displaystyle \frac{33-(0.135)(240)}{4}=0.15$ $y=0.135p+0.15$ When $p=50$ (percent), $y=0.135(50)+0.15=6.9\approx 7\quad $ (jobs created)
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.