Question

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

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

Step-by-step solution

Given information

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

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:

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

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