Question

Which of the following would provide evidence that a power law model of the form $y=a{x}^b$where $b\ne 0$and$b\ne 1$, 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 ln $y$versus $x$looks approximately linear.

(c) A scatterplot of $y$versus ln $x$looks approximately linear.

(d) A scatterplot of ln $y$versus ln $x$looks approximately linear.

(e) None of these.

Short answer

A scatterplot of in ln$y$versus in ln$x$looks approximately linear. Therefore the correct option is d.

Step-by-step solution

Given Information

A power law model of the form $y=a{x}^b$where $b\ne 0$and $b\ne 1$describes the relationship between a response variable$y$and an explanatory variable$x$.

Explanation

The scatterplot of a power model has become linear if we convert both variables to its logarithms. In the options (a) and (b) both variables are without logarithms and in the option (c) only one variable in logarithms.

Thus, the correct option is (d).