Consider the scatterplot of y versus x in Output B.6 above. a. Which power transformations on y should be considered to straighten the scatterplot? b. Which power transformations on x should be considered to straighten the scatterplot?

Question
Performing transformations
asked 2020-11-23
Consider the scatterplot of y versus x in Output B.6 above.
a. Which power transformations on y should be considered to straighten the scatterplot?
b. Which power transformations on x should be considered to straighten the scatterplot?
image

Answers (1)

2020-11-24
The provided scatter plot shows a curvature which indicates that Y values are increasing with the decrease of X values.
a. The points on y-axis indicate that power on y should be increased. There are many possible ways to straighten the scatter plot. The transformations that should be used to straighten the scatter plot is by increasing the power on Y. So, the transformed variables can be shown as y, \(y^(1.5), y^2, y^(2.5) and y^3\).
Step 2
b. The mentioned scatter plot shows that there is a negative curvilinear relationship between the variables x and y.
The arrow on the x-axis points to the left indicates that the power on x should be decreased. The transformations that should be used to straighten the scatter plot is to decrease power on X. So, the transformed variables can be shown as,
\(x,sqrtx,1/sqrtx,1/x,In (x)\)
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