Effect of Log Transformation on Linearity
A researcher considers applying a logarithmic transformation to the response variable of four data sets to achieve a more linear relationship. The characteristics of the data sets are described in the table below.
| Data Set | Description |
|---|---|
| A | Exponential growth, such as bacterial population over time |
| B | A quadratic relationship, such as free-fall distance versus time |
| C | A relationship exhibiting diminishing returns, such as income over time |
| D | An approximately linear relationship, such as daily temperature fluctuations |
Which of the following correctly ranks the data sets from the least improvement in linearity to the greatest improvement in linearity after the transformation is applied?
Free-fall distance (B), Temperature fluctuations (D), Income with diminishing returns ©, Bacterial growth (A)
Income with diminishing returns ©, Bacterial growth (A), Temperature fluctuations (D), Free-fall distance (B) (this order does not align with the expected effect of a log transformation)
Bacterial growth (A), Income with diminishing returns ©, Free-fall distance (B), Temperature fluctuations (D)
Temperature fluctuations (D), Free-fall distance (B), Income with diminishing returns ©, Bacterial growth (A)
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