MS Module 18 Units of measurement practice exam questions

(The attached PDF file has better formatting.)

[The practice problems in the 24 modules explain the statistical procedures; the practice exam questions in this thread shows what you will be asked on the final exam.]

An actuary in the United States uses least squares regression with N pairs of observations (Xi, Yi) to estimate average annual claims cost in dollars per average distance driven per day in miles, giving

annual claim costs (Y) in dollars = β0 + β1 × distance driven (X) in miles + ε, with β0 = 70 and β1 = 13.1

A European actuary changes the parameters to annual claims costs in Euros and distance driven per day in kilometers. Assume one Euro = 1.66 dollars and 1 kilometer = 0.625 miles.

Question 18.1: β0

What is β0 in the European actuary’s regression equation?

Answer 18.1: 70 / 1.66 = 42.17

($70 = €42.17)


Question 18.2: β1

What is β1 in the European actuary’s regression equation?

Answer 18.2: 13.1 × 0.625 / 1.66 = 4.93

(13.1 (dollars/mile) × (0.625 miles per kilometer) / (1.66 dollars per Euro) = 4.93 (Euros/kilometer) )