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 104: 23a

Answer

$L=52.7n+486.3$

Work Step by Step

Using desmos.com, we enter a table (columns labeled as $x_{1},y_{1}$). Then, we enter the data points, and in a new cell, enter$\quad y_{1}\sim mx_{1}+b$ The calculator returns $\left\{\begin{array}{l} m=52.7\\ b=486.3\\ r=0.9931 \end{array}\right.$ where $m=\displaystyle \frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^{2})-(\sum x)^{2}}\qquad b=\frac{\sum y-m(\sum x)}{n},$ and the $r$ is the regression cofficient $\displaystyle \quad r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{n(\sum x^{2})-(\sum x)^{2}}\cdot\sqrt{n(\sum y^{2})-(\sum y)^{2}}}$ $r$ is close to 1, indicating a good fit for the data. Replace $x_{1}\leftrightarrow n$, the independent variable, $y_{1}\leftrightarrow L$, The regression line is given by $L=52.7n+486.3$
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