Question

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

y = x +

x	y
3	17.28
4	17.04
5	17.3
6	21.46
7	21.52
8	19.38
9	22.14
10	21.7
11	22.16
12	22.92
13	21.38
14	21.54
15	25
16	23.56
17	23.32
18	24.18

Answer 1

The regression equation will be of the form,

y=β0+β1x+e ,

where β0 is the shift from the origin or the intercept and β1is the slope

of the regression equation and e is the error

Now, we have to estimate the coefficients of the equation using least square method.

Applying least square method,

β1=covx,ySx2 and β0=y-β1x

X=1ni=1nxi, Y=1ni=1nyi

X	10.5
Y	21.368
Sxx	22.667
Syy	5.9641
Sxy	9.96

Now, we have the estimated values as,

β0	16.75368
β1	0.439412

Therefore the required regression equation is,

y=16.75368+0.439412x