Explain why this graph and the graph in Problem 2.2 suggests that using log-scale is preferable if fitting simple linear regression is desired. Suppose we start with a proposed model This is a common...

Explain why this graph and the graph in Problem 2.2 suggests that using log-scale is preferable if fitting simple linear regression is desired.

Suppose we start with a proposed model

This is a common model in many areas of study. Examples include allometry (Gould, 1966), where x could represent the size of one body characteristic such as total weight and y represents some other body characteristic, such as brain weight, psychophysics (Stevens, 1966), in which x is a physical stimulus and y is a psychological response to it, or in economics, where x could represent inputs and y outputs, where this relationship is often called a Cobb– Douglas production function (Greene, 2003). If we take the logs of both sides of the last equation, we get

If we approximate
  and write
  to the extent that the logarithm of the expectation equals the expectation of the logarithm, we have

Give an interpretation of
  in this setting, assuming