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The Bulging Rule: How to Straighten Out Relationships (Mosteller & Tukey, 1977)

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The Bulging Rule: How to Straighten Out Relationships (Mosteller & Tukey, 1977). If you see this shape, use:. p >1 & q >1 . p < 1 & q > 1 . Transform x to x p &/or y to y q , where p & q are determined by the shape you see in the initial plot of y vs. x, for y>0 & x>0.

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the bulging rule how to straighten out relationships mosteller tukey 1977

The Bulging Rule: How to Straighten Out Relationships(Mosteller & Tukey, 1977)

If you see this shape, use:

p >1 & q >1

p < 1 & q > 1

Transform x to xp &/or y to yq , where p & q are determined by the shape you see in the initial plot of y vs. x, for y>0 & x>0.

That is, these plots refer to what you see in the 1st quadrant after adding appropriate constants to the original x and y so that they are both positive.

(If it’s multiple regression, transform x only.)

p >1 & q < 1

p <1 & q < 1

slide2

Transform y “up” the power ladder

“x up”

“x down”

Transform y “down” the power ladder

  • Go Up the Ladder By Taking a Power Greater Than 1
  • Down the Ladder with a Power Less Than 1
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