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46. Which of the following statements relating to Correlation and Regression are true?
(a) The Coefficient of Correlation is independent of change of origin and scale.
(b) The Coefficient of Correlation between the two variables is the arithmetic average of the two Regression Coefficients.
(c) The probable error of the Coefficient Correlation is 0.6745 times of its standard error.
(d) Coefficient of Correlation multiplied by the ratio between the standard deviations of the two variables denotes the slope of the regression line.

  • Option : B
  • Explanation : Properties of Correlation Coefficient: The following are the important properties of the coefficient of correlation:
    1. The coefficient of correlation r lies between –1 and +1, i.e., –1 £ r £ 1, i.e., a number between –1 and 1 both inclusive that describes the linear relationship between pairs of quantitative variables.
    2. The correlation coefficient is independent of the change of origin and scale.
    3. The correlation coefficient is the ratio of two quantities having same units, thus it is a pure number having no units.
    4. The value of r does not change if all the values of either variable are converted to a different scale. For example, if the units of X are changed from feet to meters, the value of r does not change.
    5. The value of r is not affected by the choice of X or Y. Interchange of all X and Y values will not change the value of r, i.e., the correlation coefficient between X and Y is equal to the correlation coefficient between Y and X.
    6. r measures the strength of linear relationship. It is not designated to measure the strength of a relationship that is not linear.
    7. If the sign of all the values of one of the variables is changed, the sign of the correlation coefficient changes, i.e., the correlation between X and Y is opposite in sign to the correlation between –X and Y or X and –Y.
    8. If each value of X and (or) Y a constant amount is added or subtracted, the correlation coefficient remains unchanged, i.e., the correlation coefficient is independent of the change of origin.
    9. If each value of X and (or) Y is multiplied or divided by a constant, the correlation coefficient remains unchanged, i.e., the correlation coefficient is independent of the change of scale.
    1. The change of origin means adding or subtracting a constant amount from given observations of the variables X and Y and the change of scale means multiplying or dividing the values of X and Y by some constant amount. The constant amount can be chosen arbitrarily as per convenience. It may be same or different for X and Y.
    2. Property II is very useful for reducing computational work involved in the calculation of the coefficient of correlation and forms the basis for short-cut method.
    Probable Error and Standard Error of Coefficient of Correlation
    The probable error (PE) of the coefficient of correlation indicates the extent to which its value depends on the condition of random sampling. If r is the calculated value of correlation coefficient in a sample of n pairs of observations, then the standard error SEr of the correlation coefficient r is given by

    The probable error of the coefficient of correlation is calculated by the expression:

    Thus with the help of PEr we can determine the range within which population coefficient of correlation is expected to fall using following formula:
    p = r ± PEr
    where p(rho) represents population coefficient of correlation.
    1. If r < PEr then the value of r is not significant, that is, there is no relationship between two variables of interest.
    2. If r > 6PEr then value of r is significant, that is, there exists a relationship between two variables.
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48. Match the items of List-II with the items of List-I and denote the code of correct matching:

(a) Testing the goodness of fit of a distribution(i) Z-test
(b) Testing the significance of the differences among the average performance of more than two sample groups(ii) Chi-square test
(c) Testing the significance of the difference between the average performance of two sample groups (Large-sized)(iii) F-test

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49. What is “Block Chain” in the field of information technology?

  • Option : B
  • Explanation : Blockchain was developed in 2008 by Satoshi Nakamoto, and was used as a core component of the digital currency, ‘bitcoin.’ Keeping the technical jargon aside, blockchain is simply a distributed and a writeonce- read-only record of digital events in a chronological order that is shared in a peerto- peer network.
    It records exchanges and transactions in a database that can be distributed and shared across authorized users that can add to it, when needed. But here’s what makes blockchain different - these authorized users can neither delete nor alter any record and no transaction can take place unless validated by all users.
    How does blockchain work?
    Blockchain is a peer-to-peer distributed ledger technology and has three major components:
    1. Distributed network: The decentralized P2P architecture has nodes consisting of network participants, where each member stores an identical copy of the blockchain and is authorized to validate and certify digital transactions for the network.
    2. Shared ledger: The members in the network record the ongoing digital transactions into a shared ledger. They run algorithms and verify the proposed transaction, and once a majority of members validate the transaction, it is added to the shared ledger.
    3. Digital transaction: Any information or digital asset that could be stored in a blockchain could qualify as a digital transaction.
    Each transaction is structured into a ‘block,’and each block contains a cryptographic hash to add the transactions in a linear, chronological order.
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50. When the organizational requirements advocate tight cost control; frequent, detailed control reports; structured organization and responsibilities and incentives based on meeting strict quantitative targets then it is called:

  • Option : D
  • Explanation : In his book, Competitive Strategy (Free Press: 1980), Michael Porter identifies three fundamental competitive strategies and lays out the required skills and resources, organizational elements and risks associated with each strategy. The table below is a shorthand way of referring to what Port has to say.
    CompetitiveStrategyRequired Skills andResourcesOrganizationalElementsAssociatedRisks
    Overall CostLeadershipSustained capital investment and access to capital.Process engineering skills.Intensive supervision of labour.Products designed for ease of manufacture. Low-cost distribution system.Tight cost controlFrequent, detailedreports.Structuredorganization andresponsibilities.Incentives based onmeeting strictquantitative targets.Technological change that nullifiespast investments or learning.Low-cost learning by industrynewcomers or followers throughimitation or through their ability toinvest in state-of-the-art facilities.Inability to see required product ormarketing change because of theattention placed on cost.Inflation in cost that narrow the firm’sability to maintain enough of a pricedifferential to offset competitors’brand images or other approaches todifferentiation.
    DifferentiationStrong marketing abilities.Product engineering.Creative flair.Strong capability inbasic research.Corporate reputation forquality or technologicalleadership.Long tradition in theindustry or unique combinationof skills drawnfrom other businesses.Strong cooperation fromchannels.Strong coordinationamong functions inR&D, product developmentand marketing.Subjective measurementand incentives insteadof quantitative measuresAmenities to attracthighly skilled labour,scientists or creativepeople.The cost differential between lowcostcompetitors and the differentiatedfirm becomes too great fordifferentiation to hold brand loyalty.Buyers thus sacrifice some of thefeatures, services, or image possessedby the differentiated firm for largecost savings.Buyers’ need for the differentiatingfactor falls. This can occur as buyersbecome more sophisticated.Imitation narrows perceived differentiation,a common occurrence asindustries mature.
    FocusCombination of theabove policies directedat the particular strategictarget.Combination of theabove policies directedat the particular strategictarget.The cost differential between broadrangecompetitors and the focusedfirm widens to eliminate the costadvantages of serving a narrow targetor to offset the differentiationachieved by focus.The differences in desired products orservices between the strategic targetand the market as a whole narrows.Competitors find submarkets withinthe strategic target and outfocus thefocuser.
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