Machine-translated by Google. Questions are authored in English.
Top

Statistics and Econometrics Questions and Answers

61.

For any pair of variables X and Y, two regression equations-one regression of Y on X and other regression of X on Y exist because

I. Tangent of the angle made by two regression equations with each other determines the coefficient of correlation.
II. Regression model does not help in the identification of dependent and independent variables of the equation.
III. Regression and correlation coefficients represent the co-variation of the two variables.
IV. Regression equation represents jointly the value of X and Y.
Select the right code from the following as the answer to the question :
Codes :

Exam Year(s)

UGC NET - 2012,

Answer: A

Two regression equations exist for a pair of variables, Y on X and X on Y, because I and II are the reasons given in the key: the angle between the two lines depends on the correlation coefficient (the lines coincide when r is plus or minus one and are at right angles when r is zero), and the regression model does not by itself identify which variable is dependent and which is independent. This is option A.

Statements III and IV describe correlation and regression in general and are not given as the reason for having two equations, so options B, C and D are not the keyed answer.

Please log in or register to report this question.

Discuss in Forum
62.

In the context of simultaneous equations econometric models, consider the following statements :

I. Identification is a problem to be dealt with before estimation.
II. Order condition is necessary but not a sufficient condition of identification.
III. Two stage least squares method of estimation gives consistent estimators if the equation is under identified.
IV. Under indirect least squares method, least squares method is applied to the reduced form equations.
Use the following code to answer the question :

Exam Year(s)

UGC NET - 2012,

Answer: D

Statements I, II and IV are correct and III is incorrect. Identification is dealt with before estimation. The order condition is necessary but not sufficient. Indirect least squares applies least squares to the reduced form equations. Two-stage least squares does not give consistent estimators when the equation is under-identified, because no estimate can be obtained for it.

So option D is right. Option A drops IV, option B accepts III, and option C accepts III and rejects IV.

Please log in or register to report this question.

Discuss in Forum
63.

If \(r_{xy} = 0.3\), match the items in list-I with the items in list-II :

List - IList - II
i. -1 to +11. 0.3
ii. Correlation coefficient between -X and Y2. Limits of correlation coefficient
iii. The Square of Correlation Coefficient3. -0.3
iv. Coefficient of correlation between -X and -Y4. Coefficient of Determination

Codes : i ii iii iv

Exam Year(s)

UGC NET - 2012,

Answer: B

The correct matches are i-2, ii-3, iii-4, iv-1. The range from -1 to +1 gives the limits of the correlation coefficient; changing the sign of one variable (between -X and Y) changes the sign of r to -0.3; the square of the correlation coefficient is the coefficient of determination; and changing the sign of both variables (between -X and -Y) leaves r at 0.3. The code is 2 3 4 1, option B.

Options A, C and D give -0.3 to the range or the square, which does not fit.

Please log in or register to report this question.

Discuss in Forum
64.

Match the following from list - I and list - II :

List - IList - II
i. Durbin-Watson 'd' Statistics1. Stationarity
ii. \(R^{2}\)2. Qualitative Effects
iii. Dickey-Fuller test3. Serial Correlation
iv. Dummy Variable4. Goodness of fit of regression function

Codes : i ii iii iv

Exam Year(s)

UGC NET - 2012,

Answer: D

The correct matches are i-3, ii-4, iii-1, iv-2. The Durbin-Watson d statistic tests serial correlation of the errors, R squared measures the goodness of fit of the regression function, the Dickey-Fuller test examines stationarity (a unit root), and a dummy variable is used for qualitative effects. The code is 3 4 1 2, option D.

Options A, B and C pair the Durbin-Watson statistic with stationarity or R squared with qualitative effects, which is wrong.

Please log in or register to report this question.

Discuss in Forum
65.

Coefficient of determination of a regression model :

1. Explains the proportion of total variation in the values of the dependent variable.
2. It can be used to derive the estimate of the extent of variation in the value of Y that is explained by the random factors.
3. Direction of inter-relation between the dependent and independent variables.
4. It explains the influence of the intercept on the dependent variable.
Select the correct code from the list given below :

Exam Year(s)

UGC NET - 2012,

Answer: B

The coefficient of determination explains the proportion of the total variation in the dependent variable (statement 1) and can be used to derive the extent of the variation in Y that is explained by the random factors, as one minus the coefficient (statement 2). So '1 and 2' is option B.

It does not show the direction of the relation between the variables (that is shown by the sign of the regression or correlation coefficient) and it does not explain the influence of the intercept, so statements 3 and 4 are wrong, and the other options are wrong.

Please log in or register to report this question.

Discuss in Forum
66.

Which of the following measures of the central tendency suits the data best if the objective is to assess the distribution of values ?

Exam Year(s)

UGC NET - 2012,

Answer: C

The keyed answer is the median. The median is the middle value when the data are in order, so it divides the distribution into two equal halves and is not pulled by a few very high or very low values, which makes it suit data that are not evenly spread. The arithmetic mean is affected by extreme values, and the mode is only the most frequent value and says little of the whole distribution. Kurtosis is not a measure of central tendency at all, since it describes the peakedness of a distribution, so option D is wrong. The keyed answer is option C.

Please log in or register to report this question.

Discuss in Forum
67.

List - IList - II
I. Simple Random Sampling1. Equal probability of selection of an item in a trial
II. Random Sampling2. Equal probability of each item in all trials
III. Stratified Random Sampling3. Random selection of first and systematic of the rest
IV. Stratified Systematic Random Sampling4. Random choice of all items from each stratum

Exam Year(s)

UGC NET - 2012,

Answer: D

The keyed matching is: simple random sampling with equal probability of each item in all trials (2), random sampling with equal probability of selection of an item in a trial (1), stratified random sampling with random choice of all items from each stratum (4), and stratified systematic random sampling with random selection of the first and systematic of the rest (3), giving 2 1 4 3, option D. The stratified systematic design picks the first item at random and the others at fixed intervals. Options A, B and C pair the stratified and systematic designs with the wrong description.

Please log in or register to report this question.

Discuss in Forum
68.

Match the following :

List - IList - II
I. Box-Jenkins Method1. Causality
II. Unit-root test2. Forecasting
III. Durbin-Watson 'd' statistic3. Stationarity
IV. Granger test4. Auto correlation

Exam Year(s)

UGC NET - 2012,

Answer: B

The matching is: Box-Jenkins method with forecasting (2), the unit root test with stationarity (3), the Durbin-Watson d statistic with auto correlation (4) and the Granger test with causality (1), giving 2 3 4 1, option B. The Box-Jenkins ARIMA method is a forecasting technique. A unit root test checks whether a series is stationary. The Durbin-Watson statistic tests for first order serial correlation in residuals. The Granger test checks whether one series helps predict another, which is causality in that sense. The other codes mispair at least two of these.

Please log in or register to report this question.

Discuss in Forum
69.

Which of the following hypotheses are tested by a regression function ?

Exam Year(s)

UGC NET - 2012,

Answer: D

A regression function tests all three kinds of hypothesis listed: whether the inter-relation between variables is significantly different from zero, whether the degree and direction of the relation are non-zero with a satisfactory goodness of fit, and whether the influence of systematic explanatory factors is greater than, lesser than or equal to the influence of random factors. These correspond to tests on the coefficients, the R squared, and the F test comparing explained with unexplained variation. Since each of A, B and C is a valid hypothesis, the keyed answer is option D.

Please log in or register to report this question.

Discuss in Forum
70.

In the presence of Heteroscedasticity, which of the following is not a correct statement ?

Exam Year(s)

UGC NET - 2012,

Answer: B

The statement that is not correct under heteroscedasticity is that the OLS estimators are of minimum variance or efficient. With non-constant error variance the OLS estimators remain unbiased and consistent, which is option A, but they are no longer efficient, because weighted least squares gives estimators with smaller variance. So option C is a true statement, and the usual t and F tests may mislead because the formulas for standard errors assume constant variance, which is option D. Option B is the false one.

Please log in or register to report this question.

Discuss in Forum
Loading…

Topics

Other Subjects

Tags: Statistics and Econometrics Questions and Answers

About Us

ExamsRepo

Copyright © 2026 ExamsRepo . All Rights Reserved . With