Question

T12.9 Which of the following would provide evidence that a power model of the form $y=a{x}^p$, where$p\ne 0$and $p\ne 1$, describes the relationship between a response variable $y$ and an explanatory variable $x$?
a. A scatterplot of $y$ versus $x$ looks approximately linear.
b. A scatterplot of $Iny$ versus $x$ looks approximately linear.
c. A scatterplot of $y$ versus $\ln x$ looks approximately linear.
d. A scatterplot of $Iny$ versus $\ln x$ looks approximately linear.
e. None of these

Short answer

The correct answer is option (d) A scatterplot of $Iny$versus $Inx$ looks approximately linear.

Step-by-step solution

Given information

To determine the relationship between a response variable $y$and an explanatory variable $x$.

Explanation

Since, the explanatory Variable also known as the independent variable.

To determine which of the following would give evidence that the relationship between a response variable y and an explanatory variable $x$is described by a power model of the type $y=a{x}^p$, where$p\ne 0,p\ne 1$.
As a result, if we convert both variables to their logarithms, the scatterplot of a power model becomes linear, and option (d) is the proper option, resulting in a scatterplot of $Iny$versus $Inx$that looks approximately linear.