The association between two variables y and x, as shown in the scatterplot above, is non-linear. Which of the following transformations is most likely to linearise the relationship?

Question

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The task is to assess which transformation would most likely produce a straight line from the given non-linear scatter.
Option a: a y^2 transformation would square the y-values and typically distort relationships further, making a curved pattern even worse for linearization rather than helping.
Option b: a 1/y transformation targets reciprocal relationships of the form y ~ 1/x. If the underlying form were hyperbolic (y decreasing with x as 1/x), this could help, but the plotted pattern does not resemble a simple reciprocal decay.
Option c: a 1/x transformation aims to linearize relationships where y is proportional to 1/x (a hyperbola). The scatter does not clearly follow a hyperbolic shape that would become linear under 1/x here.
Option d: a log y transformation is commonly used to linearize exponential-type relationships where y ≈ A · e^{B x} or to stabilize variance when growth or decay is multiplicative. Given the curved, diminishing pattern in the scatter, applying log to y is the most plausible way to straighten the trend and achieve linearity.
Thus, among the options, d. a log y transformation is the best choice for linearizing this non-linear association.

MUF0142 Fund. Mathematics Unit 2 - Semester 1, 2025 7.4 Transforming Data Quiz (Formative)

The association between two variables y and x, as shown in the scatterplot above, is non-linear. Which of the following transformations is most likely to linearise the relationship?

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