Toby observes the following coffee prices in his company cafeteria:

• 12 ounces for 1.00
• 16 ounces for 1.20
• 20 ounces for 1.40

The cafeteria announces that they will begin to sell any amount of coffee for a price that is the value predicted by a simple linear regression using least squares of the current prices on size.

Toby and his co-worker Karen want to determine how much they would save each day, using the new pricing, if, instead of each buying a 24-ounce coffee, they bought a 48- ounce coffee and shared it.

Calculate the amount they would save.

• It would cost them 0.40 more.
• It would cost the same.
• They would save 0.40.
• They would save 0.80.
• They would save 1.20.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: C

The regression line is y = 0.40 + 0.05 x. This can be obtained by either using the formula for the regression coefficients or by observing that the three points lie on a straight line and hence that line must be the solution. A 24-ounce cup costs 1.60. Two of them cost 3.20. A 48-ounce cup costs $2.80. So the savings is 0.40.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.