Question

y	x	xy	xx	yy
11.4	0	0	0	129.96
11.9	1	11.9	1	141.61
7.1	2	14.2	4	50.41
14.2	3	42.6	9	201.64
5.9	4	23.6	16	34.81
6.1	5	30.5	25	37.21
5.4	6	32.4	36	29.16
3.1	7	21.7	49	9.61
5.7	8	45.6	64	32.49
4.4	9	39.6	81	19.36
4	10	40	100	16
2.8	11	30.8	121	7.84
2.6	12	31.2	144	6.76
2.4	13	31.2	169	5.76
5.2	14	72.8	196	27.04
2	15	30	225	4
94.2	120	498.1	1240	753.66

a. Calculate SS_xx

b. Calculate β₁       

c. Calculate β₀

d. What is the Best Fit Line Equation for the 16 points based on Least Squares Linear Regression?

Answer 1

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	0	11.4	0	129.96	0
	1	11.9	1	141.61	11.9
	2	7.1	4	50.41	14.2
	3	14.2	9	201.64	42.6
	4	5.9	16	34.81	23.6
	5	6.1	25	37.21	30.5
	6	5.4	36	29.16	32.4
	7	3.1	49	9.61	21.7
	8	5.7	64	32.49	45.6
	9	4.4	81	19.36	39.6
	10	4	100	16	40
	11	2.8	121	7.84	30.8
	12	2.6	144	6.76	31.2
	13	2.4	169	5.76	31.2
	14	5.2	196	27.04	72.8
	15	2	225	4	30
Total	120	94.2	1240	753.66	498.1

(a) 340

(b) -0.6129

(c) 10.4846

(d) y' = - 0.6129x + 10.4846