You are given:

• The following observed values of the response variable, R, and predictor variables X, Y, Z:

  R	4.75	4.67	4.67	4.56	4.53	3.91	3.90	3.90	3.89
  X	M	F	M	F	M	F	F	M	M
  Y	A	A	D	D	B	C	B	D	B
  Z	2	4	1	3	2	2	5	5	1

• The following plot of the corresponding regression tree:

Calculate the Mean Response (MR) for each of the end nodes.

• MR(T1) = 4.39, MR(T2) = 4.38, MR(T3) = 4.29, MR(T4) = 3.90
• MR(T1) = 4.26, MR(T2) = 4.38,MR(T3) = 4.62, MR(T4) = 3.90
• MR(T1) = 4.26, MR(T2) = 4.39,MR(T3) = 3.90, MR(T4) = 4.29
• MR(T1) = 4.64, MR(T2) = 4.29,MR(T3) = 4.38, MR(T4) = 3.90
• MR(T1) = 4.64, MR(T2) = 4.38,MR(T3) = 4.39, MR(T4) = 3.90

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

Key: A

T1 has observations with Z ≤ 3 and Y = A or B, which are observations 1, 5, and 9. The values are 4.75, 4.53, and 3.89, which average to 4.39.

T2 has observations with Z ≤ 3 and Y = C or D, which are observations 3, 4, and 6. The values are 4.67, 4.56, and 3.91, which average to 4.38.

T3 has observations with Z > 3 and X = F, which are observations 2 and 7. The values are 4.67 and 3.90, which average to 4.29.

T4 has observations with Z > 3 and X = M, which is observation 8. The value is 3.90.

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