Estimation Of Standard Errors And Ordinary Least Square (ols)

Y N

Y*Y

X*X

X*Y

Y -mean of Y (i.e. =y)

X -mean of X(i.e. =x)

Consumption Income 1 2 3 4 5 6 7 8 9 10

sum mean

X

70 65 90 95 110 115 120 140 155 150

80 100 120 140 160 180 200 220 240 260

4900 4225 8100 9025 12100 13225 14400 19600 24025 22500

6400 10000 14400 19600 25600 32400 40000 48400 57600 67600

5600 6500 10800 13300 17600 20700 24000 30800 37200 39000

-41 -46 -21 -16 -1 4 9 29 44 39

-90 -70 -50 -30 -10 10 30 50 70 90

1110 111

1700 170

132100 13210

322000 32200

205500 20550

0 0

0 0

Dr. Sangita Y= b1+ b2x b2 = sum of xy/ sum of x square

b1 = mean of Y b2* mean of X

correln bet X and Y i.e. r =

correln bet X and estimated Y =

r square

degrees of freedom =

square of y

square of x

xy

estimated Y

u

u*u

1681 2116 441 256 1 16 81 841 1936 1521

8100 4900 2500 900 100 100 900 2500 4900 8100

3690 3220 1050 480 10 40 270 1450 3080 3510

65.18 75.36 85.55 95.73 105.91 116.09 126.27 136.45 146.64 156.82

4.82 -10.36 4.45 -0.73 4.09 -1.09 -6.27 3.55 8.36 -6.82

23.21 107.4 19.84 0.53 16.74 1.19 39.35 12.57 69.95 46.49

8890 889

33000 3300

16800 1680

1110 111

0 0

337.27 33.73

i.e. zero

0.51

24.45

method 1

SD of Y =

33.34

SD of X =

64.23

SE =Sqrt( Sqr(Y estmted Y)/n)

6.49

var =

42.16

SE = SD of Y* sqrt(1- r sqre)

0.19

4125

0.98

1

method 2

6.49 0.96

var

42.16

8

method 3

6.49

Var

SE = SE of SE/sqrt(x b2 = sqr)

42.16

0.04

var of b2 0.0013 =