Question

Movies

3

6

0

9

14

5

7

12

2

1

7

0

5

11

4

Books

7

0

18

0

1

4

5

0

6

2

10

9

2

2

0

Find the line of best fit.

r =

What is the SSE for this problem?

Answer 1

The line of best fit is

Y’ = a + bx

Where a= [(?y )(?x²) – (?x)(?xy)] / [n(?x²⁾-(?x)²]

b = [n(?xy) – (?x)( ?y)] / [n(?x²⁾-(?x)²]

x                        y                x²               y²                 xy

3	7	9	49	21
6	0	36	0	0
0	18	0	324	0
9	0	81	0	0
14	1	196	1	14
5	4	25	16	20
7	5	49	25	35
12	0	144	0	0
2	6	4	36	12
1	2	1	4	2
7	10	49	100	70
0	9	0	81	0
5	2	25	4	10
11	2	121	4	22
4	0	16	0	0
86	66	756	644	206

Therefore a = 8.1592

b = -0.6557

the equation of line of regression is

y’ = 8.1592 - 0.6557 * x

r = [n(?xy) – (?x)( ?y)] /sqrt [{n(?x²)-(?x)²}. {n(?y²)-(?y)²}] = 0.5654

sse = ?(y-y’)²

x                   y    y’=8.16-0.66x     y-y’       (y-y’)²

3	7	6.1921	0.8079	0.652702
6	0	4.225	-4.225	17.85063
0	18	8.1592	9.8408	96.84134
9	0	2.2579	-2.2579	5.098112
14	1	-1.0206	2.0206	4.082824
5	4	4.8807	-0.8807	0.775632
7	5	3.5693	1.4307	2.046902
12	0	0.2908	-0.2908	0.084565
2	6	6.8478	-0.8478	0.718765
1	2	7.5035	-5.5035	30.28851
7	10	3.5693	6.4307	41.3539
0	9	8.1592	0.8408	0.706945
5	2	4.8807	-2.8807	8.298432
11	2	0.9465	1.0535	1.109862
4	0	5.5364	-5.5364	30.65172
				240.5609

therefore

sse = 240.5609