Toby observes the following coffee prices in his company cafeteria:
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.
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.