Find an one order regression line yabx to fit the data given

Find an one order regression line (y=a+bx) to fit the data given in following Table

Solution

Here is what I did on matlab.

a =  20.4862
b = -0.8463

mean error = 2.1316e-15 almost zero

variance (error) = 5.1914

>> y = [20 18 16 15 12 9 13 14 6 4]

y =

20 18 16 15 12 9 13 14 6 4

>> y = y\'

y =

20
18
16
15
12
9
13
14
6
4

>> X = [1 2; 1 3 ; 1 5 ; 1 7 ; 1 8 ; 1 9 ;1 11; 1 13 ; 1 15 ; 1 19;]

X =

1 2
1 3
1 5
1 7
1 8
1 9
1 11
1 13
1 15
1 19

>> a = regress(Y,X)
Undefined function or variable \'Y\'.

Did you mean:
>> a = regress(y,X)

a =

20.4862
-0.8463

>> X*a

ans =

18.7936
17.9472
16.2546
14.5619
13.7156
12.8693
11.1766
9.4839
7.7913
4.4060

>> z = X*a - y

z =

-1.2064
-0.0528
0.2546
-0.4381
1.7156
3.8693
-1.8234
-4.5161
1.7913
0.4060

>> mean(z)

ans =

2.1316e-15

>> std(z)

ans =

2.2785

>> var(z)

ans =

5.1914