Econometrics Assignment Help

7/21/2019 Econometrics Assignment Help

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Econometrics Assignment Help

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Sample of Econometrics Assignment Illustrations and Solutions:

Question 1: From the data given below find,

(i) the two regression coefficients,

(ii) the correlation coefficient,

(iii) the two regression equations,

(iv)

the standard deviations of X and Y.

Expenditure on advertisement (in ’000

$) X :Volume of Sales (in lakhs $)Y :

1110

78

96

55

89

67

1011

Also, find the figure of sales when the expenditure on advertisement is $ 15000.

Solution:

Regression Analysis

X Y (X – 8)X

(Y – 8)Y

x2 y2 xy

117958610

108659711

3-11-30-22

20-2-31-13

9119044

4049119

60-29026

= 56 = 56 = 0 = 0 2 = 28 2 = 28 = 21 N = 7

We have, X = = 56/7 = 8

Y = = 56/7 = 8

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(i) (a) Regression coefficient of X on Y

This is given by

bxy =2 = 21/8 = ¾ = 0.75

(b) Regression coefficient of Y on X

This is given by

byx =2 = 21/28 = 3/4 = 0.75

(ii) Correlation Coefficient

This is given by

r = . = 0.75 × 0.75 = 0.75

(iii) The two Regression Equations

(a)X on Y: X = + (Y - )= 8 + 0.75 (Y – 8)

= 8 – 6 + 0.75Y

X = 2 + 0.75Y

(b) Y on X: Y = + byx (X - X)

= 8 + 0.75 (X – 8)

= 8 – 6 + 0.75X

Y = 2 + 0.75 X

(iv) Standard Deviation of X

This is given by

= 2

= 28

7 = 2

(v) Standard Deviation of Y

This is given by

= 2

= 28

7 = 2

Alternatively,



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bxy = r

∴ = = .75 × 2/0.75 = 2

(vi) Determination of Sales Y when Advertisement Expenditure X is $15000:

This will be determined by the regression equation of Y on X as follows:

We have, Y = 2 + 0.75X

Thus, when X = 15, Y = 2 + 0.75 (15)

= 2 + 11.25 = 13.25

∴ When X = 15000, Y = 13.25 × 1000 = $ 13250



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Question 2 :

From the data given below, compute the two regressions coefficients, and formulate the two

regression equations:

= 510, = 7140, X2

= 4150, XY = 54900,

Y2 = 740200 and N = 102.

Also, determine the value of Y when X = 7.

Solution:

(i) Two Regression Coefficients

By the value based method,

(a)

bxy = −

.

2− ()2

Putting the respective values in the above we get,

bxy =10254900− (510 ×7140)

102740200− (7140)2

=1958400

24520800 = 0.08

(b) byx = − .

2

− (

)

2


byx =10254900− (510 ×7140)

1024150− (510)2

=1958400

24520800 = 0.08

(b) byx = − . 2− ( )

2


byx =10254900− (510 ×7140)

1024150− (510)2

=1958400

163200 = 12



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(ii)Two Regression Equations

(a) X on Y: X = = =

510

102 = 5

where, X = =

510

102 = 5

And Y = Y

=7140

102 = 70

Thus, X = 5 + .08 (Y – 70)

= 5 – 5.6 + .08Y

X = -0.6 + 0.08Y

(b) Y on X: Y = Y + byx (X - X)= 70 + 12 (X – 5)

= 70 – 60 + 12X

= 10 + 12X

Y = 10 + 12X.



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(iii)Value of Y, when X = 7

When X = 7, Y = 10 + 12 (7)

= 10 + 84 = 94

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