You are given the following results from a regression model.

Observation number (i)	[math]y_i[/math]	[math]\hat{f}(x_i) [/math]
1	2	4
2	5	3
3	6	9
4	8	3
5	4	6

Calculate the sum of squared errors (SSE).

• -35
• -5
• 5
• 35
• 46

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

Key: E

Solution: SSE is sum of the squared differences between the observed and predicted values. That is,

[(2 − 4)2 + (5 − 3)2 + (6 − 9)2 + (8 − 3)2 + (4 − 6)2 ] = 46. 

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