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CFA Level I · CFA Level I Exam · Applications of Simple Linear Regression in Finance

A log-log regression of the quantity of a fund's units demanded on the fund's fee level gives ln(Quantity) = 5.2 − 1.4 × ln(Fee). Holding other factors constant, a 10% increase in the fee is most likely associated with a change in the expected quantity demanded of approximately:

In a log-log model the slope is an elasticity. With a coefficient of −1.4, a 10% rise in the fee corresponds to roughly a 14% decline in the quantity demanded, because 10 multiplied by −1.4 equals −14.

  1. A−14%.Correct
  2. B−1.4%.
  3. C+14%.

Explanation

In a log-log model the slope is an elasticity: a 1% change in X is associated with a b1% change in Y. With b1 = −1.4, a 10% fee increase implies about 10 × (−1.4) = −14% change in quantity. The −1.4% option applies the elasticity to a 1% change rather than 10%, and +14% has the wrong sign.

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