Question

Based on the data shown below, calculate the regression line (each value to two decimal places)

y =  x +

x	y
1	27.54
2	27.73
3	23.42
4	23.21
5	22.4
6	21.29
7	19.18
8	18.37
9	16.66
10	15.45
11	14.34
12	10.83
13	11.52
14	9.21
15	5.5

Answer 1

The following data are passed:

X	Y
1	27.54
2	27.73
3	23.42
4	23.21
5	22.4
6	21.29
7	19.18
8	18.37
9	16.66
10	15.45
11	14.34
12	10.83
13	11.52
14	9.21
15	5.5

The independent variable is X, and the dependent variable is Y. In order to compute the regression coefficients, the following table needs to be used:

	X	Y	X*Y	X2	Y2
	1	27.54	27.54	1	758.4516
	2	27.73	55.46	4	768.9529
	3	23.42	70.26	9	548.4964
	4	23.21	92.84	16	538.7041
	5	22.4	112	25	501.76
	6	21.29	127.74	36	453.2641
	7	19.18	134.26	49	367.8724
	8	18.37	146.96	64	337.4569
	9	16.66	149.94	81	277.5556
	10	15.45	154.5	100	238.7025
	11	14.34	157.74	121	205.6356
	12	10.83	129.96	144	117.2889
	13	11.52	149.76	169	132.7104
	14	9.21	128.94	196	84.8241
	15	5.5	82.5	225	30.25
Sum =	120	266.65	1720.4	1240	5361.9255

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

Therefore, we find that the regression equation is:

Y = 29.57 - 1.47 X