You have learned that earnings functions are one of the most investigated relationships in economics. These typically relate the logarithm of earnings to a series of explanatory variables such as education, work experience, gender, race, etc. Why do you think that researchers have preferred a log-linear specification over a linear specification?

Researchers prefer the log-linear specification because economic gains are not naturally distributed.

We can arrive at this answer because:

Within the economy, earnings are a dependent variable in relation to factors such as education, professional experiences, race, and other elements that can be considered independent variables.The distribution of earnings within an economic system is not done naturally.This promotes an increase in the error variation, which can harm an analysis with a linear method.

In this case, the use of log-linear specification can cause a more stabilized distribution that is closer to reality, promoting more precise and correct results.

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If we want to be able to explain a particular economic behaviour, we can benefit from using a linear relationship among the variables that are involved in this description. However, we can also approach this question by using a linear relationship among log-transformed variables. This is called a log-linear model.

In this example, researchers most likely prefer a log-linear specification over a linear specification because the dependent variable, which are earnings, is not normally distributed. As error variance and the variance of the dependent variable are related, this makes it difficult to state that the error variance is normally distributed. By using logarithms, we are able to get a distribution that is closer to normal.

None of them have perpendicular lines except for the blue one if I am seeing right.