Question

A linear model is given for the data in the table: y = 1.25x + 2.

x y
2 3
3 4
4 7
8 12
10 16
16 22
20 28
24 30
What is the sum of the absolute deviations?

(1 point)
Responses

7.75
7.75

8.31
8.31

11.46
11.46

2.75

Answer 1

The absolute deviations are calculated by taking the absolute difference between the predicted y value based on the linear model and the actual y value in the table for each x value.

For x = 2:
|3 - (1.25*2 + 2)| = 0.5

For x = 3:
|4 - (1.25*3 + 2)| = 0.75

For x = 4:
|7 - (1.25*4 + 2)| = 0.5

For x = 8:
|12 - (1.25*8 + 2)| = 1

For x = 10:
|16 - (1.25*10 + 2)| = 1

For x = 16:
|22 - (1.25*16 + 2)| = 2

For x = 20:
|28 - (1.25*20 + 2)| = 3

For x = 24:
|30 - (1.25*24 + 2)| = 3.5

Summing all these absolute deviations gives: 0.5 + 0.75 + 0.5 + 1 + 1 + 2 + 3 + 3.5 = 12.25

Therefore, the sum of the absolute deviations is 12.25.