The relationship between two quantities X and Y is examined,and the association is shown in the scatterplot below. What re-expression of Y should be tried as a starting point?
A)log (
Y)against X
B) $\mathrm { Y } ^ { 2 }$ against X
C) $\frac { 1 } { \log ( Y ) }$ against X
D) $\sqrt { Y }$ against X
E) $\frac { 1 } { \mathrm { Y } }$ against X

Question

The relationship between two quantities X and Y is examined,and the association is shown in the scatterplot below.  What re-expression of Y should be tried as a starting point?
A)log (
Y)against X 
B) $\mathrm { Y } ^ { 2 }$ against X 
C) $\frac { 1 } { \log ( Y ) }$ against X 
D) $\sqrt { Y }$ against X 
E) $\frac { 1 } { \mathrm { Y } }$ against X

Quizplus · Accepted Answer

Based on the scatterplot, the relationship between X and Y appears to be logarithmic. As X increases, Y also increases but at a decreasing rate. Therefore, re-expression of Y as log(Y) would be a good starting point to better visualize the relationship and potentially improve the correlation coefficient.

The Relationship Between Two Quantities X and Y Is Examined,and Y2\mathrm { Y } ^ { 2 }Y2

The Relationship Between Two Quantities X and Y Is Examined,and $\mathrm { Y } ^ { 2 }$