Question

x   y
11   7.74
9   6.61
12   12.98
10   7.14
12   7.88
13   8.68
5   6.06
4   5.24
13   8.3
7   6.61
6   5.93...

Find the equation of the regression line.

y = mx + b

Answer 1

As we know that , the formula for the regression line is

y=mx+b --------------(1)

where b is y intercept and m is the slope of the given equation.

Firstly, we need to find m and b.

So the formula for m = (n(Σxy)-(Σx)(Σy)) / (nΣx² -(Σx)²) --------------(2)

where n is the number of samples =11

Σx= 11+9+12+10+12+13+5+4+13+7+6=102

Σy=7.74+6.61+12.98+7.14+7.88+8.68+6.06+5.24+8.3+6.61+5.93= 83.17

Σx²= 121+81+144+100+144+169+25+16+169+49+36=1054

Σxy=11*7.74+9*6.61+12*12.98+10*7.14+12*7.88+13*8.68+5*6.06+4*5.24+13*8.3+7*6.61+6*5.93 =820.2

From eq 2,

m=11*820.2-(102)(83.17)/ 11*1054-(1054)²

=>m=538.86/1190

=>m=0.4528

Now we have to find y intercept b,

The formula for b= ------------------(3)

= Mean of y sample

= Mean of x sample

  

From equation (3)

b=7.5609- 0.4528*9.2727 (m=0.4528)

=>b=3.3623

Therefore y=mx+b

=>y=0.4528x + 3.3623