Statistics and Econometrics Questions and Answers

Q: Regression coefficient is independent of change in

The regression coefficient is independent of change in origin but not of scale.If a constant is added to or subtracted from every value of x or y, the regression coefficient does not change, since the deviations from the mean are the same. If the values are multiplied by a constant, as in a change of units, the coefficient changes, since it depends on the units of both variables.So it is independent of origin and not of scale, and the other options reverse or deny this.

Q: Suppose that observations are available on the monthly bond prices of 100 companies for five years. What type of data are these ?

The data are panel data.Observations on the same 100 companies, each followed over five years (monthly bond prices), combine a cross-section of companies with a time series for each. Such data are called panel or longitudinal data.Cross-sectional data would be one point in time and time series data a single company over time, and the data are not qualitative since bond prices are numbers.

Q: What is the meaning of the term "heteroscedasticity" ?

Heteroscedasticity means that the variance of the errors is not constant.In the classical regression model the error variance is the same for all observations (homoscedasticity). When it varies from one observation to another, the errors are heteroscedastic.Errors that are not independent of one another describe autocorrelation, and errors with a non-zero mean describe a mis-specified model or a missing intercept. The variance of the dependent variable is not the definition.

Q: Which of the following estimation techniques are available for the estimation of over-identified systems of simultaneous equations ?(i) OLS (ii) ILS(iii) 2SLS (iv) IVCodes :

The techniques available are (iii) and (iv) only, 2SLS and IV.For an equation that is over-identified, there is more than one way of getting each structural coefficient from the reduced form, so indirect least squares does not give a unique answer. Two-stage least squares and instrumental variables use the extra instruments and give consistent estimates.OLS applied directly is inconsistent because of the correlation of the regressors with the errors, and ILS applies only to exactly identified equations.

91.

Assertion (A) : Fisher's index is an ideal index.

Reasoning (R) : Fisher's index satisfies Time Reversal and Factor Reversal Tests.
Codes :

A.Both (A) and (R) are true and (R) is correct explanation of (A).
B.Both (A) and (R) are true, but (R) is not correct explanation of (A).
C.(A) is true, but (R) is false.
D.(A) is false, but (R) is true.

Exam Year(s)

UGC NET - 2013,

Answer: A

Both the assertion and the reason are true and the reason explains the assertion. Fisher's index is called an ideal index because it satisfies both the time reversal test and the factor reversal test, which most other indices do not satisfy together; it is the geometric mean of the Laspeyres and Paasche indices. So (A) is correct, and the options that call either statement false are wrong. The two tests are time reversal, by which interchanging the base and the current period gives reciprocal indices, and factor reversal, by which the product of price and quantity indices equals the value ratio.

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92.

Match Group - I with Group - II :

Group - I	Group - II
a. Variance	i. Sampling distribution
b. Mode	ii. Normal distribution
c. \(\chi^{2}\) distribution	iii. Measure of dispersion
d. Mesokurtic distribution	iv. Measure of central tendency

Codes : a b c d

A.i iii ii iv
B.iii iv i ii
C.ii iv iii i
D.iv ii i iii

Exam Year(s)

UGC NET - 2013,

Answer: B

Variance is a measure of dispersion (iii). The mode is a measure of central tendency (iv). The chi-square distribution is a sampling distribution (i). The mesokurtic distribution, which has the kurtosis of the normal curve, is the normal distribution (ii). So a-iii, b-iv, c-i, d-ii, which is code B. The other codes give the mode or variance to the wrong class.

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93.

Assertion (A) : Fisher's Index No. is ideal Index No.

Reason (R) : Fisher's Index satisfies time reversal and factor reversal tests.
Codes :

A.Both (A) and (R) are true and (R) is the correct explanation of (A).
B.Both (A) and (R) are true, but (R) is not correct explanation of (A).
C.(A) is true, but (R) is false.
D.(A) is false, but (R) is true.

Exam Year(s)

UGC NET - 2013,

Answer: A

Both statements are true and the reason explains the assertion. Fisher's index number is called the ideal index because it satisfies both the time reversal test and the factor reversal test, which most other formulae fail to meet together. It is the geometric mean of the Laspeyres and Paasche indices. So the reason is the correct explanation of the assertion, which is the first option.

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94.

There are 12 white balls, 8 red balls and 5 green balls in a basket. What is the probability that a ball drawn is either red or white ?

A.12/25
B.8/25
C.20/25
D.15/25

Exam Year(s)

UGC NET - 2013,

Answer: C

There are 12 + 8 + 5 = 25 balls in all, and 12 + 8 = 20 of them are red or white. The two events are mutually exclusive, so:

\[ P = \frac{12}{25} + \frac{8}{25} \]

\[ P = \frac{20}{25} \]

So the probability is 20/25, which is the third option. The options 12/25 and 8/25 are the probabilities of a white ball or a red ball alone, and 15/25 has no basis in the data.

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95.

Coefficient of determination is given as

A.\(r/1 - r^{2}\)
B.\(1 - r^{2}\)
C.\(1 + r^{2}\)
D.\(r^{2}\)

Exam Year(s)

UGC NET - 2013,

Answer: D

The coefficient of determination is the square of the correlation coefficient, r squared. It shows the proportion of the variation in the dependent variable that is explained by the regression. The expression 1 minus r squared is the proportion left unexplained, called the coefficient of non-determination. The other options, r divided by (1 minus r squared) and 1 plus r squared, are not standard measures. So r squared is the answer. Its value lies between zero and one, so a value of 0.81 means that 81 percent of the variation is explained.

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96.

For testing the equality of population variances the test to be applied is

A.Student's t test
B.\(\chi^{2}\) test
C.F distribution
D.Z distribution

Exam Year(s)

UGC NET - 2013,

Answer: C

To test the equality of two population variances the F test is used, as the ratio of the two sample variances follows the F distribution when the population variances are equal. Student's t test compares means, the chi-square test is used for the variance of one population or for goodness of fit and independence, and the Z test compares means or proportions for large samples. So the F distribution is the answer. The variance ratio test of Fisher is applied with the larger variance in the numerator and has degrees of freedom of the two samples.

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97.

Regression coefficient is independent of change in

A.origin but not of scale
B.both origin and scale
C.scale but not of origin
D.none of these

Exam Year(s)

UGC NET - 2013,

Answer: A

The regression coefficient is independent of change in origin but not of scale.

If a constant is added to or subtracted from every value of x or y, the regression coefficient does not change, since the deviations from the mean are the same. If the values are multiplied by a constant, as in a change of units, the coefficient changes, since it depends on the units of both variables.

So it is independent of origin and not of scale, and the other options reverse or deny this.

Discuss in Forum

98.

Suppose that observations are available on the monthly bond prices of 100 companies for five years. What type of data are these ?

A.Cross Sectional
B.Time Series
C.Panel
D.Qualitative

Exam Year(s)

UGC NET - 2013,

Answer: C

The data are panel data.

Observations on the same 100 companies, each followed over five years (monthly bond prices), combine a cross-section of companies with a time series for each. Such data are called panel or longitudinal data.

Cross-sectional data would be one point in time and time series data a single company over time, and the data are not qualitative since bond prices are numbers.

Discuss in Forum

99.

What is the meaning of the term "heteroscedasticity" ?

A.The variance of errors is not constant.
B.The variance of dependent variable is not constant.
C.The errors are not linearly independent of one another.
D.The errors have non-zero mean.

Exam Year(s)

UGC NET - 2013,

Answer: A

Heteroscedasticity means that the variance of the errors is not constant.

In the classical regression model the error variance is the same for all observations (homoscedasticity). When it varies from one observation to another, the errors are heteroscedastic.

Errors that are not independent of one another describe autocorrelation, and errors with a non-zero mean describe a mis-specified model or a missing intercept. The variance of the dependent variable is not the definition.

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100.

Which of the following estimation techniques are available for the estimation of over-identified systems of simultaneous equations ?

(i) OLS (ii) ILS
(iii) 2SLS (iv) IV
Codes :

A.(iii) only
B.(iii) and (iv) only
C.(ii), (iii) and (iv) only
D.(i), (ii), (iii) and (iv)

Exam Year(s)

UGC NET - 2013,

Answer: B

The techniques available are (iii) and (iv) only, 2SLS and IV.

For an equation that is over-identified, there is more than one way of getting each structural coefficient from the reduced form, so indirect least squares does not give a unique answer. Two-stage least squares and instrumental variables use the extra instruments and give consistent estimates.

OLS applied directly is inconsistent because of the correlation of the regressors with the errors, and ILS applies only to exactly identified equations.

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