Question

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

y =  x +

x	y
4	13.72
5	18.65
6	17.38
7	17.41
8	20.44
9	21.97
10	21.5
11	20.63
12	25.16
13	22.29
14	24.82
15	24.65

Answer 1

Solution:
Regression equation can be written as
Y = a + b*x
Here a is intercept of regression line
Y is dependent Variable
X is independent variable
b is the slope of regression line

X	Y	X^2	Y^2	XY
4	13.72	16	188.2384	54.88
5	18.65	25	347.8225	93.25
6	17.38	36	302.0644	104.28
7	17.41	49	303.1081	121.87
8	20.44	64	417.7936	163.52
9	21.97	81	482.6809	197.73
10	21.5	100	462.25	215
11	20.63	121	425.5969	226.93
12	25.16	144	633.0256	301.92
13	22.29	169	496.8441	289.77
14	24.82	196	616.0324	347.48
15	24.65	225	607.6225	369.75
114	248.62	1226	5283.0794	2486.38

Slope of regression line can be calculated as
Slope = ((n*Xi*Yi) - (Xi * Yi))/((n*Xi^2) - (Xi)^2)) = ((12*2486.38) - (114*248.62))/((12*1226)-(114)^2)) = 1493.88/1716 = 0.87
Intercept of regression line can be calculated as
Intercept = (Yi - Slope Xi)/n = (248.62 - 0.87*114)/12 = 12.45
So regression equation is
Y = 12.45 + 0.87*X