Question

1. Find the SSE for the given data and linear models, and indicate which model gives the better fit.

(0,1) (1,1) (2,2) (4,3)

1. Y = 0.4x + 1.1                                                   SSE = ________
2. Y = 0.5x + 0.9                                                   SSE = ________
3. The better fit is          Y = ____________

2. Given the data

(0,40) (1,60) (2,70) (3,50) (4,60) (5,75) (6,90), (7,80), (8,85)

find:

Sum of x = ______ Sum of y = ______

Sum of  xy = ______ Sum of  x2 = ______ Sum of y2 = _______       

Regression line: ______________________

Correlation Coefficient: ____________

Answer 1

1)

a)

x	y	y'	(y-y')^2
0	1	1.1	0.01
1	1	1.5	0.25
2	2	1.9	0.01
4	3	2.7	0.09
		total	0.36

SSE =0.36

b)

x	y	y'	(y-y')^2
0	1	0.9	0.01
1	1	1.4	0.16
2	2	1.9	0.01
4	3	2.9	0.01
		total	0.19

SSE =0.19

c) since SSE for line b is better: better fit is Y =0.5x+0.9

2)

Sum of x =36

Sum of y =610

Sum of  xy = 2745

Sum of  x2 = 204

Sum of y2 =43550

Regression line: y^ =5.0833x+47.444

Correlation Coefficient: 0.8384