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Q. 45

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The Practice of Statistics for AP

Found in: Page 791

Book edition 4th

Author(s) David Moore,Daren Starnes,Dan Yates

Pages 809 pages

ISBN 9781319113339

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Short Answer

Suppose that the relationship between a response variable y and an explanatory variable x is modelled by $y = 2.7 {(0.316)}^{x}$ . Which of the following scatterplots would approximately follow a straight line?
(a) A plot of y against x
(b) A plot of y against log x
(c) A plot of log y against x
(d) A plot of log y against log x
(e) None of (a) through (d)

The scatterplots that approximately follow a straight line is option (c) A plot of log y against x.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

The relationship between a response variable y and an explanatory variable x is modelled by $y = 2.7 {(0.316)}^{x}$ .

Step 2: Explanation

The given equation is

$y = 2.7 {(0.316)}^{x}$

The scatterplot will not be a straight line since this equation represents an exponential function, which is not linear.

If we multiply both sides of the equation by the logarithm, we get:

$\log y = \log [2.7 (0.316)^{x}] = \log 2.7 + \log 0 . 316^{x} = \log 2.7 + x \log 0.316$

This is a linear equation with variables log $y$ and $x$ and thus the scatterplot will be a straight line in this case.

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