UGC NET ECONOMICS · 2022 · UNIT 3
Statistics and Econometrics PYQs
सांख्यिकी और अर्थमिति के प्रश्न
December2021/June2022 merged · 8October2022
दिसंबर2021/जून2022 संयुक्त · 8अक्टूबर2022
Regression and econometrics
प्रतिगमन और अर्थमिति
Question 6 / प्रश्न 6
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The fitted regression equation is given by Yi = –10 + 0.6X. What is the value of the residual at the point X = 40, Y = 60
Ŷ=−10+.6X में observed X40, Y60 का residual?
(a) 74
(b) 46
(c) 0
(d) 45
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (b) 46
Explanation: The fitted value is14; the residual is60−14=46.
व्याख्या: Fitted value−10+.6×40=14। Residual observed−fitted=60−14=46। Fitted minus observed sign उलटा होगा।
Question 13 / प्रश्न 13
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What are the practical consequences of multicollinearity in CLRM? A. R2, the overall measure of grodness of fit can be very high B. OLS estimators are not BLUE C. OLS estimators have small variance and covariances D. t ratio of one or more coefficients is statistically insignificant E. The OLS estimators and their standard errors can be sensitive to small changes in the data
Multicollinearity: A high R²; B OLSnot BLUE; C small variance; D insignificantt; E small data change पर sensitive।
(a) A, B और C केवल
(b) A, B और D केवल
(c) A, D और E केवल
(d) B, C और E केवल
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (c) A, D और E केवल
Explanation: Imperfect collinearity can inflate variances and destabilise estimates without destroying BLUE under the other assumptions.
व्याख्या: A D E common symptoms हैं। Imperfect collinearity में Gauss Markov assumptions हों तो OLSBLUE रहता है, लेकिन coefficient variance large होती है। Perfect collinearity में unique OLS ही नहीं।
Question 22 / प्रश्न 22
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A simultaneous equation model is said to be over-identified if.
Structural equation overidentified का सही अर्थ?
(a) केवल एक independentidentifyingrestriction।
(b) एकसेअधिक independentidentifyingrelations।
(c) हर structuralcoefficientunidentifiable।
(d) Estimation असम्भव।
Answer & Explanation / उत्तर और व्याख्या
उत्तर: wording सुधारकर
Explanation: Overidentification means excess valid identifying restrictions, not multiple true population parameter values.
व्याख्या: Overidentification में more valid instruments/restrictions than minimum needed होते हैं, full rank के साथ। Population parameter true values multiple नहीं होते; different instrument sets finite-sample estimates दे सकते हैं।
Descriptive statistics
वर्णनात्मक सांख्यिकी
Question 62 / प्रश्न 62
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Hari's score in the statistics in the first year is 76, whereas the class average is 68 with a standard deviation of 5. What is Hari's Z-score?
Score76, mean68, SD5 में zscore?
(a) 1.5
(b) 1.6
(c) 1.2
(d) 1.4
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (b) 1.6
Explanation: (76−68)/5=1.6.
व्याख्या: z=(76−68)/5=1.6। Score mean से 1.6standard deviations ऊपर है; zdimensionless है।
Probability and distributions
प्रायिकता और वितरण
Question 64 / प्रश्न 64
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A bag contains 20 tickets marked with numbers 1 to 20. One ticket is drawn at random. Find the probability that will be multiple of 2 or 5.
1 से 20 ticket में multiple of2 OR5 की probability?
(a) 0.7
(b) 0.9
(c) 0.6
(d) 0.8
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (c) 0.6
Explanation: There are10multiples of2and4of5, with2overlaps; 12/20=.6.
व्याख्या: 2multiples10,5multiples4, दोनों के multiples10 व 20=2। Union count10+4−2=12; probability12/20=.6।
Question 65 / प्रश्न 65
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Normal-distribution statements: A Q₁+Q₂=2Md (Q₂ printed for upper quartile); B QD=σ/3; C QD=2σ/3; D all odd central moments are zero; E Q₁+Q₂+Md (incomplete).
Normal distribution: A lower+upperquartiles=2median; B QD=σ/3; C QD≈2σ/3; D odd central moments zero; E printedquartileexpressionincomplete।
(a) B, D और E केवल
(b) A, B, D केवल
(c) A, C और D केवल
(d) C, D और E केवल
Answer & Explanation / उत्तर और व्याख्या
उत्तर: approximation के साथ
Explanation: Normal QD=.67449σ, approximately2σ/3; the upper-quartile label also needs interpretation.
व्याख्या: Normal QD=.67448975σ≈2σ/3, exact equality नहीं। Symmetry से Q₁+Q₃=2Md और odd central moments0। Source Q₂ को upperquartilelabel करता है; conventional Q₂=median लेंतो A का notationwrong होगा।
Question 83 / प्रश्न 83
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The binomial distribution can be used under the following conditions A. n the number of trials is finite and independent B. n the number of trials is infinite and independent C. Each trial results in two mutually exclusive and exhaustive outcomes, terms as success and failure D. P, the probability of success is constant for each trial E. The probability of failure does not remain same for each trial
Binomial: A finite independent trials; B infinite trials; C success/failure exclusive exhaustive; D constantp; E failureprobchanges।
(a) A, C, और E केवल
(b) B, C, और D केवल
(c) A, C, और D केवल
(d) B, C, और E केवल
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (c) A, C, और D केवल
Explanation: A binomial count requires finite independent trials, two outcomes, and constant success probability.
व्याख्या: A C D n-trial Bernoullisum की assumptions हैं। Failureprob1−p भी constant होगी। Infinite count नहीं, finitefixedn है।
Time series
काल श्रेणी
Question 73 / प्रश्न 73
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Write the steps to estimate the ECM/VAR model in time series. A. Unit root test B. ACF and PACF test C. ECM/VAR D. Inputting data E. Cointegration test
ECM/VARsteps: A unit root; B ACF/PACF; C estimate ECM/VAR; D load data; E cointegration।
(a) D, A, E, B, C
(b) D, B, A, C, E
(c) D, B, A, E, C
(d) B, A, D, E, C
Answer & Explanation / उत्तर और व्याख्या
उत्तर: एक valid work flow
Explanation: Data, exploration, integration tests, cointegration, and appropriate model ling form a valid work flow, not a unique rigid sequence.
व्याख्या: Ddata → Bexploratorydependence → Aintegration → E cointegration → Cmodel। ACF/PACF को unit root test के बादभीदेखसकते हैं; essential dependency cointegration assessment before appropriate ECM/VECM specification है, unique all-purpose order नहीं।
Statistical inference
सांख्यिकीय अनुमान
Question 78 / प्रश्न 78
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Match List I with List II.
Tests match करें।
| ListI सूचीI |
ListII सूचीII |
|---|---|
| A Overallregressionsignificance समग्रमहत्त्व |
I Chisquare काईवर्ग |
| B Attributeindependence गुणोंकी स्वतंत्र ता |
II Jarque Bera जार्कबेरा |
| C Individualcoefficient व्यक्तिगुणांक |
III Ftest एफपरीक्षण |
| D Normality सामान्यता |
IV ttest टीपरीक्षण |
(a) I II III IV
(b) III I IV II
(c) I IV III II
(d) I III IV II
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (b) III I IV II
Explanation: Overall F, attributeχ², individualt, and Jarque–Bera normality determine the intended matches.
व्याख्या: Overall joint slopes F, contingency tableχ², individualcoefficientt और skewness/kurtosis-based normality JB। Source Cgeneral“regression” को individual coefficient test पढ़नेपर matching है।
December2022 · 2March2023 · ShiftI
दिसंबर2022 · 2मार्च2023 · पालीI
Probability and distributions
प्रायिकता और वितरण
Question 13 / प्रश्न 13
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Find the variance of random variables which constitute the number of heads in a toss coins simultaneously.
Simultaneous coins में heads count की variance?
(a) 1/2
(b) 1
(c) 2
(d) 4
Answer & Explanation / उत्तर और व्याख्या
Explanation: Fair-coin head-count variance is n/4; the printed question omitsn, so.5requires two coins.
व्याख्या: nindependentfaircoins में X~Binomial(n,.5), Var X=n/4। n2 होतो.5option(a)। Printed stem coins की संख्या नहीं देता है, इसलिए unconditionalnumericanswer नहीं मिलता।
Question 20 / प्रश्न 20
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A box of nine golf gloves contains two left handed and seven right-handed gloves. If two gloves are randomly selected from the box without replacement, what is the probability that one is left-handed and the other is a right- handed glove?
2left/7right gloves में without replacement2draw करएक left एक right की probability?
(a) 7/12
(b) 2/9
(c) 7/18
(d) 1/9
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (c) 7/18
Explanation: 2×7/C(9,2)=7/18.
व्याख्या: Favourable C(2,1)C(7,1)=14, total C(9,2)=36 ⇒14/36=7/18। Ordered route2×(2/9)(7/8)भी same देती है।
Question 47 / प्रश्न 47
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Which are correct? A E(c)=0; B E(X+Y)=E(X)+E(Y); C Var(X±c)=Var(X); D independent X, Y imply E(XY)=E(X)E(Y); E Var(a X)=a Var(X).
Expectation: A E(c)=0; B E(X+Y)=EX+EY; C Var(X±c)=Var X; D independent XYfactorises; E Var(a X)=a Var X।
(a) A, B और D केवल
(b) B, D और E केवल
(c) B, C और D केवल
(d) B, C और E केवल
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (c) B, C और D केवल
Explanation: E(c)=c and Var(a X)=a²Var(X); linearity and the stated independence result give B, C, D.
व्याख्या: B C D सही। E(c)=c और Var(a X)=a²Var X। Expectation linearity में independence नहीं चाहिए, productfactorisation के लिएयह sufficient condition है।
Question 49 / प्रश्न 49
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Which of the following are correct in case of area under the standard normal probability curve. A. Distance from the mean of ordinates in terms of ± σ at Z = ± 0.6745 is 0.55 B. Distance from the mean ordinates in terms of ± σ at Z = ± 1.96 is 0.95 C. Distance from the mean ordinates in terms of ±σat Z = 2.0 is 0.9544 D. Distance from the mean ordinates in terms of ± σ at Z = ± 2.58 is 0.98 E. Distance from the mean ordinates in terms of ± σ at Z = ± 3.0 is 0.9973
Central normal areas: A±.6745=.55; B±1.96=.95; C±2=.9544; D±2.58=.98; E±3=.9973।
(a) A, C और E केवल
(b) B, C और E केवल
(c) B, C और D केवल
(d) A, B और E केवल
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (b) B, C और E केवल
Explanation: The central normal areas are approximately.50,.95,.9545,.9901, and.9973.
व्याख्या: ±.6745 area≈.50,±1.96≈.95,±2≈.9545,±2.58≈.9901,±3≈.9973। इसलिए B C E standardrounding में सही।
Question 59 / प्रश्न 59
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For independent events A, B: A P(A|B)=P(A); B P(A|B)=P(B); C P(A∩B)=P(A)P(B); D P(A∩B̄)=P(A)P(B̄); E P(Ā∩B̄)=P(Ā)P(B).
Independent A, B की statements और complements मेंकौन सही ?
(a) B, C और E केवल
(b) A, C और D केवल
(c) B, C और D केवल
(d) A, C और E केवल
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (b) A, C और D केवल
Explanation: Independent events also have independent complements; A, C, D hold after restoring the bars.
व्याख्या: A condition P(B)>0 पर true; C independence product; D complements की independence से true। E में LHS दो complements हैं लेकिन RHSBuncomplemented है, इसलिए false generally।
Time series
काल श्रेणी
Question 16 / प्रश्न 16
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Test statistics used to test stationary of a time series in the presence of correlated error term is.
Seriallycorrelatederrors के साथ unit root test कौन?
(a) Dickey-Fuller test
(b) Engle-Granger test
(c) Error-correction mechanism
(d) Augmented Dickey-Fuller test
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (d) Augmented Dickey-Fuller test
Explanation: ADF adds lagged differences to control serially correlated disturbances when testing a unit root.
व्याख्या: ADF regression lagged differences add करके residual autocorrelation control करती है। H₀unit root है; stationary alternative के critical values non standard हैं।
Regression and econometrics
प्रतिगमन और अर्थमिति
Question 17 / प्रश्न 17
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In logit model as Pi goes from 0 to 1, logit L varies from.
p0 से 1 जानेपर logit ln[p/(1−p)] की range?
(a) 0 to+∞
(b) −∞ to+∞
(c) 0 to1
(d) −∞ to0
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (b) −∞ to+∞
Explanation: Log odds span−∞to+∞as probability moves from0to1.
व्याख्या: p→0 पर logit→−∞; p→1 पर+∞। Logit all real numbers लेसकता है, probability0–1bounded रहती है।
Question 19 / प्रश्न 19
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The regression model Yt = α1+α2 Dt + β1Xt + β2 (Yt Dt) + Ut is used to.
Y=α₁+α₂D+β₁X+β₂(YD)+u का intended purpose?
(a) Deseasonaliseonly।
(b) Seasonaltrendonly।
(c) Structuralbreak।
(d) Continuouspiecewiseonly।
Answer & Explanation / उत्तर और व्याख्या
उत्तर: interactiontypo सुधारकर
Explanation: The intended structural-break model needs XD, not the printed dependent-variable interaction YD.
व्याख्या: Standard break model intercept dummy D और slope interaction XD use करता है। Printed YD dependent variable को RHS मेंलाता है, जिससे standard OLSinterpretation बदलती है। Intendedc के लिएβ₂XD होना चाहिए।
Question 48 / प्रश्न 48
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Which of the following are correct are OLS estimation in the presence of autocorrelation? A. The estimated coefficients are linear B. The estimated coefficients are unbiased C. The estimated coefficients are biased D. The estimated coefficients are consistent E. The estimated coefficients are efficients
Autocorrelation only, strictly exogenous X में OLS: A linear; B unbiased; C biased; D consistent; E efficient।
(a) A, C और D केवल
(b) A, B और D केवल
(c) A, C और E केवल
(d) C, D और E केवल
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (b) A, B और D केवल
Explanation: Autocorrelation alone need not bias exogenous-regressor OLS, but generally invalidates efficiency and usual standard errors.
व्याख्या: A B D under usual regularity conditions। Seriallycorrelatederrors covarianceΩ≠σ²I से OLS generally inefficient और usual SEinvalid होते हैं। Lagged dependent variables/endogeneity होतो unbiasedness/consistency बचनेकी guarantee नहीं।
Question 50 / प्रश्न 50
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Which of the following satisfy the assumptions of the classical linear regression model? A. The regression model is linear in the parameters B. Zero mean value of disturbance Ui C. The variance of Ui is constant D. There is a serial autocorrelation between the disturbance terms E. The number of observations must be greater than the number of parameters to be estimated
CLRM: A linear parameters; B zero conditional error; C constant variance; D serial autocorrelation; E observations>parameters।
(a) B, C और E केवल
(b) A, B और E केवल
(c) B, D और E केवल
(d) A, C और D केवल
Answer & Explanation / उत्तर और व्याख्या
उत्तर: पूरा option नहीं
Explanation: A, B, C, E belong to the classical model; the complete combination is missing.
व्याख्या: A B C E classical model assumptions/estimabilityconditions में हैं; D no autocorrelation केविरुद्ध है। Source(b)A B E homoscedasticity C छोड़ता है। Zero unconditional mean alone केबजाय E(u|X)=0 चाहिए।
Question 68 / प्रश्न 68
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Match List I with List II.
Econometric models match करें।
| ListI सूचीI |
ListII सूचीII |
|---|---|
| A Censoredregression censored प्रतिगमन |
I Probit प्रोबिट |
| B Normit नॉर्मिट |
II Marc Nerlove नेर्लोव |
| C Distributedlag वितरितपश्चता |
III Tobit टोबिट |
| D Partialadjustment आंशिकसमायोजन |
IV L M Koyck कॉयक |
(a) A-I, B-III, C-II, D-IV
(b) A-III, B-I, C-IV, D-II
(c) A-III, B-IV, C-I, D-II
(d) A-IV, B-III, C-I, D-II
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (b) A-III, B-I, C-IV, D-II
Explanation: Censoring maps to Tobit, normit to Probit, lags to Koyck, and partial adjustment to Nerlove.
व्याख्या: Tobitlatentoutcomecensoring; normit=probit; Koyck geometric lags; Nerlove partial adjustment। AIII BI CIV DII।
Question 69 / प्रश्न 69
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Match List I with List II.
Functional forms और point elasticities match करें।
| ListI सूचीI |
ListII सूचीII |
|---|---|
| A Y=β₁+β₂X | I β₂X |
| B ln Y=β₁+β₂X | II β₂ |
| C Y=β₁+β₂ln X | III β₂X/Y |
| D ln Y=β₁+β₂ln X | IV β₂/Y |
(a) A-III, B-IV, C-I, D-II
(b) A-III, B-I, C-IV, D-II
(c) A-II, B-I, C-III, C-IV
(d) A-II, B-III, C-IV, D-I
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (b) A-III, B-I, C-IV, D-II
Explanation: Applying elasticity=(d Y/d X)X/Y yields the four displayed formulas.
व्याख्या: Elasticity=(d Y/d X)X/Y। Linearβ₂X/Y; loglinβ₂X; linlogβ₂/Y; log logβ₂। AIII BI CIV DII।
December2022 · 2March2023 · ShiftII
दिसंबर2022 · 2मार्च2023 · पालीII
Probability and distributions
प्रायिकता और वितरण
Question 8 / प्रश्न 8
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For two events A, B that need not be independent, which formula is valid?
Dependent A, B की joint probability का general formula?
(a) P(A∩B)=P(A)P(B)
(b) P(A∩B)=P(A)P(B|A)
(c) P(A∩B)=P(A)P(A|B)
(d) P(A∩B)=1−P(A∪B)
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (b) P(A∩B)=P(A)P(B|A)
Explanation: The general multiplication rule is P(A∩B)=P(A)P(B|A).
व्याख्या: Multiplication rule P(A∩B)=P(A)P(B|A), P(A)>0। Independent case में conditional P(B|A)=P(B) होता है; यहाँ वह replace नहीं कर सकते।
Question 16 / प्रश्न 16
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A player tosses two fair coins. He wins Rs. 5 if 2 heads occurs, Rs. 2 if 1 head occurs and Rs. 1 if no head occurs. Find his expected gain.
2fair coins:2heads₹5,1head₹2,0heads₹1 में expectedwinning?
(a) ₹2
(b) ₹2.25
(c) ₹2.75
(d) ₹2.50
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (d) ₹2.50
Explanation: 5/4+2/2+1/4=₹2.50expected gross winnings.
व्याख्या: Probabilities¼,½,¼। E=5/4+2/2+1/4=2.50। Entry fee दिया नहीं; यह expectedgrosswinning है।
Question 17 / प्रश्न 17
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A card is thrown from a well shuffled pack of playing cards. Find the probability that it is either a diamond or a king. 17 16
52-card deck में diamond OR king probability?
(a) 17/52
(b) 16/52
(c) 18/52
(d) 15/52
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (b) 16/52
Explanation: 13diamonds+4kings−1overlap gives16/52.
व्याख्या: 13diamonds+4kings−1diamond king=16favourable cards। P16/52=4/13। Intersection को twice count नकरें।
Question 45 / प्रश्न 45
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Which of the followings are correct in case of Poisson distribution? A. ‘n’ the number of trials is indefinitely large i.e. n → ∞ B. ‘p’, the constant probability of success for each trial is indefinitely large C. np = m is finite D. μ3 = m + 2 E. μ4 = m + 3m2
Poisson limit: A n→∞; B p→large; C np=mfinite; D μ3=m+2; E μ4=m+3m²।
(a) A, C और D केवल
(b) A, C और E केवल
(c) B, C और E केवल
(d) B, C और D केवल
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (b) A, C और E केवल
Explanation: Poisson’s binomial limit hasn→∞, p→0, np=m; centralμ4=m+3m².
व्याख्या: Rare-eventbinomiallimitn→∞, p→0, np=m। Poisson centralμ3=m,μ4=m+3m²। इसलिए A C E।
Regression and econometrics
प्रतिगमन और अर्थमिति
Question 14 / प्रश्न 14
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In logit model, as the odds ratio decreases from 1 to 0, the logit becomes.
Odds1 से 0 घटनेपर logitln(odds)?
(a) Negative।
(b) हमेशा zero।
(c) Positive।
(d) केवल fraction।
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (a) Negative।
Explanation: The logarithm of odds between0and1is negative.
व्याख्या: Odds1 पर logit0 और 0<odds<1 पर log negative होता, odds→0 पर−∞। Probability और odds कोएकनसमझें।
Question 15 / प्रश्न 15
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Given regression model as Yi = α1 + β1 Xi + β2 (Xi –X*) Di + Ui such a model is used to.
Y=α+β₁X+β₂(X−X*)D+u काउपयोग?
(a) Quarterlydeseasonalising।
(b) Monthlyadjustmentonly।
(c) General Chowwithoutrestrictionsonly।
(d) Continuouspiecewiselinearrelation।
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (d) Continuouspiecewiselinearrelation।
Explanation: The interaction creates a continuous slope change at the threshold X*.
व्याख्या: D=1when X>X*लेनेपर kink X*पर continuous होती है। Slopesβ₁औरβ₁+β₂, लेकिन jump नहीं। β₂=0 slope same क atest है।
Question 18 / प्रश्न 18
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In simultaneous equation models. OLS can be applied directly if.
SEM में direct equation wise OLS कब valid हो सकता है?
(a) Recursivewithappropriateuncorrelatederrors।
(b) Orderconditionalone।
(c) Rankconditionalone।
(d) Identificationconditionsalone।
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (a) Recursivewithappropriateuncorrelatederrors।
Explanation: Recursive equations need appropriate cross-equation error orthogonality for direct OLS.
व्याख्या: Triangular recursive causal ordering और cross-equationerrororthogonality में RHSendogenousvariables equation error से uncorrelated हो सकते हैं। Recursivityalone correlated structural errors के साथ OLSconsistent नहीं बनाती।
Question 47 / प्रश्न 47
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Which of the followings are correct for OLS estimation in the presence of Heteroscedasticity? A. The estimated coefficients are linear B. The estimated coefficnets are unbiased C. The estimated coefficients are biased D. The estimated coefficients are consistent E The estimated coefficients are efficient
Heteroscedasticity only/exogenous X में OLS: A linear; B unbiased; C biased; D consistent; E efficient।
(a) A, C और D केवल
(b) A, B और D केवल
(c) A, C और E केवल
(d) A, C और D केवल
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (b) A, B और D केवल
Explanation: Exogenous-regressor OLS remains linear, unbiased, and consistent under heteroscedasticity, but generally not efficient.
व्याख्या: A B D correct under regularity conditions। Unequal error variance alone bias नहीं लाती; OLSgenerallyinefficient और usualhomoscedastic SEinvalid होती है। Robust SEinference सुधारती है।
Question 48 / प्रश्न 48
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Which of the followings satisfy the assumptions of the classical linear regression model? A. Zero mean value of disturbance ui B. The explanatory variables and the error terms are not independent C. Homoscedasticity or constant variance of ui D. No auto corrletion between the disturbances. E. There is more than one exact linear relationship between explanatory variables.
CLRM: A zero conditional error; B regressor/error non independence claim; C constant variance; D no autocorrelation; E exact collinearity।
(a) A, B, C और D केवल
(b) A, C, D और E केवल
(c) A, C और D केवल
(d) C, D और E केवल
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (c) A, C और D केवल
Explanation: Zero conditional errors, homoscedasticity, and no autocorrelation fit the intended classical assumptions.
व्याख्या: A C D intended। Coreexogeneity E(u|X)=0 है; full statistical independence हमेशा जरूरी नहीं। Eexactlinearrelationshipsuniquecoefficientestimation तोड़ती हैं।
Question 50 / प्रश्न 50
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In multiple regression model, a hypothesis such as H0: β2 = β3 = 0 can be tested using.
Joint H0:β2=β3=0 कोकौन test करेगा?
(a) Individualttest।
(b) Chisquareonly।
(c) ANOVAasgenericlabel।
(d) Partial Ftest।
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (d) Partial Ftest।
Explanation: A joint two-coefficient exclusion uses a partial Ftest rather than separate individualttests.
व्याख्या: Twojointrestrictionsq2 के लिए F=[(RSSr−RSSu)/2]/[RSSu/(n−ku)]। Separate5%ttestsjoint5%test केबराबर नहीं। Robustsettings में Wald test alternative है।
Question 66 / प्रश्न 66
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Match List I with List II.
Diagnostics match करें।
| ListI सूचीI |
ListII सूचीII |
|---|---|
| A Serialcorrelation क्रमिकसहसंबंध |
I Goldfeld–Quandt गोल्डफेल्डक्वांट |
| B Heteroscedasticity विषमप्रसरण |
II Runstest रनपरीक्षण |
| C Multicollinearity बहुसहरेखीयता |
III Ramsey RESET रैम्ज़ीरीसेट |
| D Specification विनिर्देशन |
IV Conditionindex अवस्थासूचकांक |
(a) A-III, B-I, C-IV, D-I
(b) A-II, B-IV, C-I, C-III
(c) A-IV, B-I, C-III, D-II
(d) A-I, B-IV, C-III, D-II
Answer & Explanation / उत्तर और व्याख्या
उत्तर: कोई option नहीं
Explanation: The correct match is A-II, B-I, C-IV, D-III; none of the listed codes matches.
व्याख्या: Runstest residual sign randomness, Goldfeld Quandt variance comparison, condition index collinearity, RESET functional form diagnostic। Book explanation की matching सही है लेकिन marked(c)codes गलत हैं।
Statistical inference
सांख्यिकीय अनुमान
Question 46 / प्रश्न 46
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Which of the followings are correct conclusions without error in case of testing of hypothesis? A. Reject null hypothesis (H0), when it is true B. Accept H0, when it is true C. Accept H0, when Alternative hypothesis (H1) is true D. Reject Ho when H1 is true. E. Accept H0 when H1 is false.
Correct test decisions: A reject true H0; B retain true H0; C retain when H1true; D reject when H1true; E retain when H1false।
(a) A, B और D केवल
(b) B, D और E केवल
(c) B, C और E केवल
(d) A, C और E केवल
Answer & Explanation / उत्तर और व्याख्या
उत्तर: (b) B, D और E केवल
Explanation: Retaining a true null or rejecting a false null avoids error; retention is not proof of truth.
व्याख्या: B D E error-free outcomes हैंजब H0/H1exhaustive हों। Atype I और Ctype IIerror है। Statistical terminology में“fail to reject”कहें; data H0 को prove नहीं करते।