The Reciprocal Transformation (VCE SSCE General Mathematics): Flashcards

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The Reciprocal Transformation
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Purpose of reciprocal transformation

Linearise non-linear data

Reciprocal vs logarithmic transformation compression

Reciprocal gives more dramatic compression

Reciprocal transformation of xx

1x\frac{1}{x}

Reciprocal transformation of yy

1y\frac{1}{y}

When to use reciprocal transformation

Curved relationship between variables needs straightening

Effect of 1x\frac{1}{x} on larger xx values

Compresses larger values relative to smaller values

Reversal property of reciprocal transformation

Reverses data order around 1 (values <1 become >1, vice versa)

Back-transform needed with 1x\frac{1}{x} transformation?

No, substitute directly into equation

Critical step for 1y\frac{1}{y} transformation predictions

Back-transform by taking reciprocal of calculated value

What reciprocal transformation compresses

Upper end of scale on x-axis or y-axis

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