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Return-unit scaling and a fitted slope

Converting both return series from percentages to decimals preserves beta; converting only one changes its numeric slope.

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Use the original economic observations

The displayed benchmark percentage numbers are −2/−1/0/1/2 and asset numbers −3/−0.5/1/2.5/6. Their slope is 2.1 and intercept 1.2 percentage points per period.

Convert both sides consistently

Dividing both lists by 100 preserves slope 2.1, while intercept becomes 0.012 in decimal-return units. Correlation and R² are unchanged because this is a common positive unit transformation.

Inspect a one-sided conversion

Original unit representations
X input unitY input unitNumeric slope
Percentage numbersPercentage numbers2.1
Decimal returnsDecimal returns2.1
Decimal returnsPercentage numbers210
Percentage numbersDecimal returns0.021

Retain the calculator’s input convention

The public fields are percentage-labeled and convert both sides consistently. Entering decimal-return numbers as if they were percentages changes the record. A large or small fitted slope cannot repair an incorrect source-unit label.

Further references