APFIVE In a study of population growth, a researcher observed a curved (nonlinear) relationship between Year (x) and Population (y in 1000s). To linearize the relationship, the student decided to apply a logarithmic transformation. However, instead of transforming the independent variable (Year), the student mistakenly applied the log transformation to the Population values. What is the mistake in this approach?
| Year | Population (1000s) |
|---|---|
| 1980 | 44 |
| 1990 | 65 |
| 2000 | 101 |
| 2010 | 150 |
| 2020 | 230 |
They failed to center the data around the mean before applying the transformation.
They should have applied a square root transformation rather than a logarithmic one.
They transformed the dependent variable instead of the independent variable, thereby distorting the intended linear relationship.
They correctly applied the transformation to linearize the non‐linear relationship.
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