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Q. 45

Expert-verifiedFound in: Page 791

Book edition
4th

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

Pages
809 pages

ISBN
9781319113339

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.

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

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:

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

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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