Question

DATA 1

ID	X1	Y
A	0	9
B	1	10
C	0	5
D	1	1
E	0	0

The zero order model is Ŷ = 8 − 2.5X1

1. What is the residual error in using the zero order model to predict Y for ID C? (Correct answer is -3, please show me how to find it)

2. What is the error in using the mean of Y to predict Y for ID C? (correct answer is -2, please show me how to find it)

Answer 1

1).when x=0,

$\hat{y}=$ 8-(2.5 * 0)= 8

y=5

residual error for ID C = (observed value - predicted value) = (5-8)= -3

2).mean of y=(9+10+5+1+0)/5 =25/5 =5

when x1=mean of y =5,

$\hat{y}=$ 8 - (2.5*5) = 8-12.5 =4.5

error for ID C = (observed value - predicted value) = (5 - 4.5) = 0.5

**********BUT I THINK IN ORDER TO GET THE ANSWER -2,YOUR QUESTION SHOULD BE:

What is the error in using the mean of X to predict Y for ID C?

now ,i am solving this:

mean of x = (0 + 1+ 0+ 1 +0)/5 = 2/5 =0.4

when x1=mean of x = 0.4,

$\hat{y}=$ 8 - (2.5* 0.4) = 8-1 = 7

error for ID C = (observed value - predicted value) = (5-7) = -2

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