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Chapter 12: Q. 45 (page 791)

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)

Short Answer

Expert verified

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

Step by step solution

01

Given information

The relationship between a response variable y and an explanatory variable x is modelled byy=2.7(0.316)x.

02

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:

logy=log2.7(0.316)x=log2.7+log0.316x=log2.7+xlog0.316

This is a linear equation with variables log yand xand thus the scatterplot will be a straight line in this case.

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