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Why Choose Us? Accuracy: We are a company employed with highly qualified Economics experts to ensure fast and accurate homework solutions aimed at any difficult homework – both Micro economics and Macro economics. Econometrics Assignment Sample Questions and Answers: Question 1: From the following bivariate frequency distribution, obtain the two regression equations and estimate the marks in Statistics of a student who secures 40 marks in Quantitative Techniques. Also, find the coefficient of correlation between the two variables. X Y Marks in Q.T. (Y)
Marks in Statistics (X) 20-25 25-30 30-35 Total 16-20 20-24 24-28 Total
9 6 15
14 11 25
3 7 10
23 20 7 50
Solution According to the table given, marks in statistics are represented by X and marks in Q-T are represented by Y. Thus, the regression analysis in the given problem will be made as follows : Correlation Table (Vide Page 409) Required factors (i)Arithmetic average of the X variable :
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Fd ′x
X=A+
N
Ă— đ?‘–đ?‘Ľ
= 27.5 + -5/50 × 5 = 27 (ii)Arithmetic average of the Y variable : Fd′y
Y=A+
đ?‘
Ă— đ?‘–đ?‘Ś
= 22 + -16/50 Ă— 4 = 20.72 (iii)Regression coefficient of X on Y : bxy =
N N
=
Fd x d y − . Fd x . Fd y Fd y 2 − ( Fd y 2 )
50 Ă—16−(−5 Ă— −16) 50 Ă—30−(−16)2
=
800 −80 1500 −256
Ă—
5 4
Ă—
đ?‘–đ?‘Ľ đ?‘–đ?‘Ś
Ă— 5/4
= 0.72
(iv)Regression coefficient of Y on X : byx =
đ?‘
=
Fd x d y − đ?‘
Fd x . Fd y
Fd đ?‘Ľ 2 − ( Fd x 2 )
50 Ă—16−(−5 Ă— −16)
=
50 Ă—25 − (−5)2 800 −80 1250 −25
Ă—
đ?‘–đ?‘Ś đ?‘–đ?‘Ľ
Ă— 4/5
Ă— 4/5 = 0.47
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(a)Regression Equations (i) Of X on Y This is given by X = X + bxy (Y - Y) = 27 + 0.72(Y – 20.72) = 27 – 14.9184 + 0.72Y = 12.0816 + 0.72Y ∴
X = 12.0816 + 0.72
(ii)of Y on X This is given by Y = Y + byx (X - X) = 20.72 + 0.47 (X – 27) = 20.72 – 12.69 + 0.47 X = 8.03 + 0.47 X ∴
Y = 8.03 + 0.47X
Thus, the two regression equations are : X = 12.0816 + 0.72 T and
Y = 8.03 + 0.47 X
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(b)Estimation of marks in statistics (X) When the marks in Q.T. (Y) = 40, X = 12.0816 + 28.80 = 12.0816 + 28.80 = 30.8816 = 31 approx.
(c)Coefficient of Correlation Basing upon the regression coefficients we have, r = đ?‘?đ?‘Ľđ?‘Ś . đ?‘?đ?‘Śđ?‘Ľ = 0.72 Ă— 0.47 = 0.3384 or 0.34
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