A scatterplot of $\frac { 1 } { \sqrt { y } }$ vs. x shows a strong positive linear pattern. It is probably true that
A) accurate predictions can be made for $\mathrm { Y }$ even if extrapolation is involved.
B) the correlation between $\mathrm { X }$ and $\mathrm { Y }$ is near $+ 1.0$.
C) large values of $X$ are associated with large values of $Y$.
D) the scatterplot of $\mathrm { Y }$ vs $\mathrm { X }$ also shows a linear pattern.
E) the residuals plot for regression of $Y$ on $X$ shows a curved pattern.

Question

Quizplus · Accepted Answer

The transformation $\frac{1}{\sqrt{y}}$ vs. x showing a linear pattern suggests that the original relationship between Y and X is non-linear, likely requiring transformation for linear regression, hence a curved pattern in residuals.

A Scatterplot Of 1y\frac { 1 } { \sqrt { y } }y​1​

A Scatterplot Of $\frac { 1 } { \sqrt { y } }$