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Chapter 12 Introduction to Statistical Methods and Econometrics 
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Part – I
Multiple Choice questions
Question 1.
The word ‘statistics’ is used as ……………..
a) Singular
b) Plural
c) Singular and Plural
d) None of above
Answer:
c) Singular and Plural
Question 2.
Who stated that statistics as a science of estimates and probabilities.
a) Horace Secrist
b) R. A Fisher
c) Ya – Lun – Chou
d) Boddington
Answer:
d) Boddington
Question 3.
Sources of secondary data are ……………..
a) Published sources
b) Unpublished sources
c) neither published nor unpublished sources
d) Both (A) and (B)
Answer:
d) Both (A) and (B)
Question 4.
The data collected by questionnaires are ………………….
a) Primary data
b) Secondary data
c) Published data
d) Grouped data
Answer:
a) Primary data
Question 5.
A measure of the strength of the linear relationship that exists between two variables is called:
a) Slope
b) Intercept
c) Correlation coefficient
d) Regression equation
Answer:
c) Correlation coefficient
Question 6.
If both variables X and Y increase or decrease simultaneously, then the coefficient of correlation will be:
a) Positive
b) Negative
c) Zero
d) one
Answer:
a) Positive
Question 7.
If the points on the scatter diagram indicate that as one variable increases the other variable tends to decrease the value of r will be :
a) Perfect positive
b) Perfect negative
c) Negative
d) Zero
Answer:
c) Negative
Question 8.
The value of the coefficient of correlation r lies between :
a) 0 and 1
b) 1 and 0
c) 1 and +1
d) 0.5 and +0.5
Answer:
c) 1 and +1
Question 9.
The term regression was used by :
a) Newton
b) Pearson
c) Spearman
d) Galton .
Answer:
d) Galton .
Question 10.
The purpose of simple linear regression analysis is to:
a) Predict one variable from another variable
b) Replace points on a scatter diagram by a straightline
c) Measure the degree to which two variables are linearly associated
d) Obtain the expected value of the independent random variable for a given value of the dependent variable
Answer:
a) Predict one variable from another variable
Question 11.
A process by which we estimate the value of dependent variable on the basis of one or more independent variables is called:
a) Correlation
b) Regression
c) Residual
d) Slope
Answer:
b) Regression
Question 12.
If Y = 2 – 0.2 X, then the value of Yintercept is equal to
a)0.2
b) 2
c) 0.2 X.
d) All of the above
Answer:
b) 2
Question 13.
In the regression equation Y = Î²_{0}+ Î²_{1} X, the Y is called
a) Independent variable
b) Dependent variable
c) Continuous variable
d) none of the above
Answer:
b) Dependent variable
Question 14.
In the regression equation X =Î²_{0}+ Î²_{1} X, the X is called :
a) Independent variable
b) Dependent variable
c) Continuous Variable
d) none of the above
Answer:
a) Independent variable
Question 15.
Econometrics is the integration of
a) Economics and Statistics
b) Economics and Mathematics
c) Economics, Mathematics, and Statistics
d) None of the above
Answer:
c) Economics, Mathematics, and Statistics
Question 16.
Econometric is the word coined by
a) Francis Gal ton
b) RagnarFrish
c) Karl Person
d) Spearsman
Answer:
b) RagnarFrish
Question 17.
The raw materials of Econometrics are :
a) Data
b) Goods
c) Statistics
d) Mathematics
Answer:
a) Data
Question 18.
The term Uiin regression equation is
a) Residuals
b) Standard error
c) Stochastic error term
d) none
Answer:
c) Stochastic error term
Question 19.
The term Uiis introduced for the representation of
a) Omitted Variable
b) Standard error
c) Bias
d) Discrete Variable
Answer:
a) Omitted Variable
Question 20.
Econometrics is the amalgamation of
a) 3 subjects
b) 4 subjects
c) 2 subjects
d) 5 subjects
Answer:
a) 3 subjects
PARTB
Answer the following questions in one or two sentences.
Question 21.
What is Statistics?
Answer:
 The term‘Statistics’is used in two senses: as singular and plural.
 In singular form it simply means statistical methods.
 Statistics when used in singular form helps in the collection, presentation, classification and interpretation of data to make it easily comprehensible.
 In its plural form it denotes collection of numerical figures and facts.
 In the narrow sense it has been defined as the science of counting and science of averages.
Question 22.
What are the kinds of Statistics?
Answer:
 Descriptive statistics
 Inferential statistics
Question 23.
What do you mean by Inferential Statistics?
Answer:
 The branch of statistics concerned with using sample data to make an inference about a population of data is called Inferential Statistics.
 It draws conclusion for the population based on the sample result.
 It uses hypotheses, testing and predicting on the basis of the outcome.
 It tries to understand the population beyond the sample.
Question 24.
What are the kinds of data?
Answer:
Data may be classified Based on characteristics.
 Quantitative Data
 Qualitative Data Based on sources:
 Primary Data
 Secondary Data.
Question 25.
Define Correlation.
Answer:
Correlation is a statistical device that helps to analyse the covariation of two or more variables. Sir Francis Galton, is responsible for the calculation of correlation coefficient.
Question 26.
Define Regression.
Answer:
Regression means going back and it is a mathematical measure showing the average relationship between two variables.
Question 27.
What is Econometrics?
Answer:
Origin Of Econometrics:
 Economists tried to support their ideas with facts and figures in ancient times.
 Irving Fisher is the first person, developed mathematical equations in the quantity theory of money with help of data.
 Ragnar Frisch, a Norwegian economist and statistician named the integration of three subjects such that mathematics, statistical methods, and economics as Econometrics” in 1926.
PART – C
Answer the following questions in one paragraph.
Question 28.
What are the functions of Statistics?
Answer:
Functions of Statistics:
 Statistics presents facts in a definite form.
 It simplifies mass of figures.
 It facilitates comparison.
 It helps in formulating and testing.
 It helps in prediction.
 It helps in the formulation of suitable policies.
(I) Statistics are an aggregate of facts:
For example, numbers in a calendar pertaining to a year will not be called statistics, but to be included in statistics it should contain a series of figures with relationships for a prolonged period.
(II) Statistics are numerically enumerated, estimated and expressed.
(III) Statistical collection should be systematic with a predetermined purpose:
The purpose of the collection of statistics should be determined beforehand in order to get accurate information.
(IV) Should be capable of being used as a technique for drawing comparison:
It should be capable of drawing comparisons between two different sets of data by tools such as averages, ratios, rates, coefficients etc.
Question 29.
Find the Standard Deviation of the following data: 14, 22, 9, 15, 20, 17, 12, 11
(Answer: = 4.18)
Question 30.
State and explain the different kinds of Correlation.
1) Based on the direction of changÃ© of variables:
 Positive correlation
 Negative correlation
2) Based upon the number of variables studied:
 Simple correlation
 Multiple correlations
3) Partial correlation
Based upon the constancy of the ratio of change between the variables:
 Linear correlation 1
 Nonlinear correlation
Question 31.
Mention the uses of Regression Analysis.
Answer:
 Regression means going back and it is a mathematical measure showing the average relationship between two variables.
 Both the variables may be random variables.
 It indicates the cause and effect relationship between the variables and establishes a functional relationship.
 Besides verification, it is used for the prediction of one value, in relation to the other given value.
 The regression coefficient is an absolute figure. If we know the value of the independent variable, we can find the value of the dependent variable.
 In regression, there is no such spurious regression.
 It has wider application, as it studies linear and nonlinear relationships between the variables.
 It is widely used for further mathematical treatment.
Question 32.
Specify the objectives of econometrics.
Answer:
 It helps to explain the behaviour of a forthcoming period that is forecasting economic phenomena.
 It helps to prove the old and established relationships among the variables or between the variables.
 It helps to establish new theories and new relationships.
 It helps to test the hypotheses and estimation of the parameter.
Question 33.
Differentiate the economic model with the econometric model.
Answer:
Economic Model:
 Economic model is the theoretical construct that represents the complex economic process.
 Economic model is based on mathematical modeling.
 Economic model is focused on establishing the logical relationships between the variables in the model.
 Economic model is applied in stating the theoretical relationship into mathematical equations.
 Economic model believes that the outcome is certain and exact. So disturbance term is not required.
 Economic model is deterministic in nature.
 The Keynesian consumption function: C = a + by is the economic model
Econometric Model:
 Econometric model is the statistical concept that represents the numerical estimate of the variables involved in economic process.
 Econometric model is based on statistical modeling.
 Econometric model is focused on estimating the magnitude and direction of relationship between the variables.
 Econometric model is applied in stating the empirical extent of the economic model.
 Econometric model believes that outcome is certain but not exact. So disturbance term plays the vital role.
 Econometric model is stochastic in nature.
 The Keynesian consumption function: C = a + by + Âµ is the econometric model
Question 34.
Discuss the important statistical organizations (offices) in India.
Answer:
 The Ministry of statistics has two wings, statistics and programme Implementation.
The statistics wing called the National Statistical office (NSO) consists of the central Statistical office ((SO), the computer center and the National Sample Survey office (NSSO).  There is also National Statistical commission created through a Resolution of Government of India and an autonomous Institute (ie) Indian Statistical Institute.
Question 35.
Elucidate the nature and scope of Statistics.
Answer:
Nature of Statistics:
 Different Statisticians and Economists differ in views about the nature of statistics, some call it a science and some say it is an art.
 Tippett on the other hand considers Statistics both as a science as well as an art.
Scope of Statistics:
Statistics is applied in every sphere of human activity – social as well as physical – like Biology, Commerce, Education, Planning, Business Management, Information Technology, etc.
Statistics and Economics:
 Statistical data and techniques are immensely useful in solving many economic problems
 Such as fluctuation in wages, prices, production, distribution of income and wealth and so on.
Statistics and Firms:
Statistics is widely used in many firms to find whether the product is conforming to specifications or not.
Statistics and Commerce:
 Statistics are the lifeblood of successful commerce.
 Market survey plays an important role to exhibit the present conditions and to forecast the likely changes in future.
Statistics and Education:
 Statistics is necessary for the formulation of policies to start new courses, according to the changing environment.
 There are many educational institutions owned by public and privately engaged in research and development work to test the past knowledge and evolve new knowledge.
 These are possible only through statistics.
Statistics and Planning:
1. Statistics is indispensable in planning. In the modem world, which can be termed as the “world of planning”, almost all the organisations in the government are seeking the help of planning for efficient working, for the formulation of policy decisions and execution of the same.
2. In order to achieve the above goals, various advanced statistical techniques are used for processing, analyzing and interpreting data.
3. In India, statistics play an important role in planning, both at the central and state government levels, but the quality of data highly unscientific.
Statistics and Medicine:
 In Medical Sciences, statistical tools are widely used. In order to test the efficiency of a new drug or to compare the efficiency of two drugs or two medicines, a ttest for the two samples is used.
 More and more applications of statistics are at present used in clinical investigation.
Statistics and Modern applications:
 Recent developments in the fields of computer and information technology have enabled statistics to integrate their models and thus make statistics a part of the decisionmaking procedures of many organisations.
 There are many software packages available for solving simulation problems.
Question 36.
Calculate the Karl Pearson Correlation Coefficient for the following data
Answer : r = 0.9955
Question 37.
Find the regression equation Y on X and X on Y for the following data:
(Answer : Y = 0.787X + 7.26, and X = 0.87Y + 26.65)
Question 38.
Describe the application of Econometrics in Economics.
Answer:
 To forecast macroeconomics indicators:
Econometrical methods are used to forecast macroeconomic indicators, Time – series models can be used to make predictions about economic indicators.  To Support Mathematical Economic Model:
Tinbergen points out that “Econometrics as a result of certain outlook on the role of economics, consists of the application of mathematical statistics to economic data to lend empirical support to the models constructed by mathematical economics and to obtain numerical results.’  Econometric methods are used for the firms in a number of ways like to determine minimum wage rate, factors responsible for the firm to remain in the market, Market Functions etc.
12th Economics Guide Introduction to Statistical Methods and Econometrics Additional Important Questions and Answers
I. Match the following:
Question 1.
a) Contribution to vital statistics – 1) Kautilya
b) Father of statistics – 2) GP Nelson
c) Arthashastra – 3) Akbar’s rule
d) ‘Am – .e – Akbari – 4) Ronald Fisher
Answer:
c) 3 4 1 2
Question 2.
a) Quantitative Data – 1) Collected for the first time
b) Qualitative Data – 2) Data from NSSO
c) Primary Data – 3) Number of firms
d) Secondary Data – 4) Gender
Answer:
c) 3 4 1 2
II. Choose the correct pair
Question 1.
a) Mean – Special Average
b) Geometric Mean – Simple Average
c) Standard Deviation – Root mean square deviation
d) Dispersion – frequency deviation
Answer :
c) Standard Deviation – Root mean square Deviation
Question 2.
a) Correlation – Irving Fisher
b) Regression – Karl Pearson
c) Quantity theory – Francis Dalton
d) Econometrics – Ragnar Frisch
Answer:
d) Econometrics – Ragnar Frisch
III. Choose the incorrect pair
Question 1.
a) Statistics Day – June 29
b) NSSO – 1960
c) P. C. Mahalanobis – father of statistics in India.
d) Central Statistical office – New Delhi
Answer :
b) NSSO 1960
Question 2.
a) Positive correlation – Y = a – bx
b) Simple correlation – Y = a + bx
c) Non linear correlation – Y = a + bx^{2}
d) Multiple correlation – Qd = f (p, P_{c},P_{s}, t, y)
Answer:
a) Positive correlation – Y = a – bx
IV. Pick the odd one out
Question 1.
a) Scatter diagram method
b) Graphic Method
c) Karl Pearson’s coefficient of regression
d) Method of least squares
Answer:
c) Karl Pearson’s coefficient of regression
Question 2.
a) Simple correlation
b) Multiple correlations
c) Partial correlation
d) Positive correlation
Answer:
d) Positive correlation
V. Choose the correct statement
Question 1.
a) Correlation means “stepping back towards the Average”
b) Universal law of regression was given by Karl Pearson
c) Econometrics is concerned with the empirical determination of economic laws.
d) Econometrics is the integration of economics and mathematics.
Answer:
c) Econometrics is concerned with the empirical determination of economic laws
Question 2.
a) Mathematics is a science of estimates and probabilities.
b) Tipett considered statistics as a science.
c) Karl Pearson introduced the concept of standard deviation
d) Correlation is a statistical device that helps to analyse the covariation of two or more variables.
Answer:
d) Correlation is a statistical device that helps to analyse the covariation of two or more variables.
VI. Choose the incorrect statement
Question 1.
a) Sir Francis Galton, is responsible for the calculation of the correlation coefficient.
b) If three variables are taken for study it is called a simple correlation.
c) Indian statistical institute is declared as an Institute of National importance by as Act of parliament.
d) The ministry of statistics and programme Implementation came into existence in 1999
Answer:
b) If three variables are taken for study it is called a simple correlation.
Question 2.
a) Econometrics may be considered as the integration of economics, statistics
and Accountancy
b) Ragnar Frish was awarded the Nobel prize in 1969.
c) The coefficient of correlation is a relative measure.
d) Regression is used for the further mathematical treatment of the variables.
Answer:
a) Econometrics may be considered as the integration of economics, statistics, and Accountancy.
VII. Fill in the blanks.
Question 1.
The term statistics originated in the Latin word known as ………………………….
(a) Statistik
(b) Status
(c) Statistique
(d) Statistics
Answer:
(b) Status
Question 2.
“Statistics is a science of estimates and probabilities” is a statement of …………………
a) Ronald Fisher
b) Boddington
c) Croxton
d) Cowdeg
Answer:
b) Boddington
Question 3.
The first book to have statistics as its title was ………………………….
(a) Contributions to vital statistics
(b) Principles of statistics
(c) Statistics principles
(d) Statistics probabilities
Answer:
(a) Contributions to vital statistics
Question 4.
To test the efficiency of a new drug or to compare the efficiency of two drugs ………….. test in used.
a) ttest
b) ftest
c) chitest
d) None
Answer:
a) ttest
Question 5.
The branch of statistics devoted to the summarization and description of data is called …………….. statistics.
a) Interential
b) Descriptive
c) hypothetical
d) None
Answer:
b) Descriptive
Question 6.
Who is the father of statistics?
(a) Gottfried Achenwall
(b) Francis GP. Nelson
(c) Ronald Fisher
(d) R.A. Fisher
Answer:
(d) R.A. Fisher
Question 7.
Karl Pearson introduced the concept of standard deviation is ………………….
a) 1891
b) 1892
c) 1893
d) 1894
Answer :
c) 1893
Question 8.
Statistics are the lifeblood of success………………………….
(a) Maths
(b) Datas
(c) Calculations
(d) Commerce
Answer:
(d) Commerce
VIII. Answer the following in one or two sentences.
Question 1.
Write five averages?
Answer:
 There are five averages.
 Among them mean, median, and mode are called simple averages and the other two averages geometric mean and harmonic mean are called special averages.
Question 2.
What is partial correlation?
Answer:
If there are more than two variables but only two variables are considered keeping the other variables constant, then the correction is said to be a partial correlation.
Question 3.
Write the kinds of dispersion?
Answer:
There are two kinds of measures of dispersion, namely
 The absolute measure of dispersion
 A relative measure of dispersion
Question 4.
Mention the methods of studying the correlation.
Answer:
 Scatter diagram method.
 Graphic method.
 Karl person’s coefficient of correlation
 Method of least squares.
Question 5.
State the formula to compute Karl person coefficient of correlation.
Answer:
Question 6.
Explain the advantages of the Scatter diagram method?
Answer:
Advantages of the Scatter Diagram method:
 It is a very simple and nonmathematical method
 It is not influenced by the size of an extreme item.
 It is the first step in resting the relationship between two variables.
Question 7.
What are the types of Averages?
Answer:
There are five averages. Mean, median, and mode are called simple averages and geometric mean and harmonic mean are called special averages.
IX. Answer the following question in paragraph
Question 1.
Differentiate Descriptive and Inferential statistics.
Answer:
Descriptive Statistics  Inferential Statistics 
It describes the population under study.  It draws conclusions for the population based on the sample result. 
It presents the data in a meaning ful way through charts, diagrams, graphs, other than described in words.  It uses hypotheses, testing, and predicting on the basis of the outcome. 
It gives a summary of data.  It tries to understand the population beyond the sample. 
Question 2.
Briefly explain the kinds of measures of dispersion?
Answer:
There are two kinds of measures of dispersion, namely
 The absolute measure of dispersion
 A relative measure of dispersion
The absolute measure of dispersion indicates the amount of variation in a set of values in terms of units of observations. Relative measures of dispersion are free from the units of measurements of the observations. They are pure numbers. They are used to compare the variation in two or more sets, which are having different units of measurements of observations. Standard Deviation is one of the methods of Absolute measure of dispersion.
Karl Pearson introduced the concept of standard deviation in 1893. Standard deviation is also called Root Mean Square Deviation. The reason is that it is the square – root of the mean of the squared deviation from the arithmetic mean. It provides accurate results. The Square of standard deviation is called Variance.
Question 3.
Explain the Characteristics of statistics.
Answer:
 Statistics are an aggregate of facts.
 Statistics are numerically enumerated, estimated, and expressed.
 The statistical collection should be systematic with a predetermined purpose.
 Should be capable of being used as a technique for drawing a comparison.
Question 4.
What are the limitations of statistics?
Answer:
 Statistics is not suitable to the study of the qualitative phenomenon
 Statistical laws are not exact.
 The statistics table may be misused.
 Statistics is only one of the methods of studying a problem.
Question 5.
Write a short note on NSSO.
Answer:
The National sample survey organization, now known as the National sample survey office, is an organization under the ministry of statistics of the Government of India. It is the largest organization in India, conducting regular socioeconomic surveys. It was established in 1950.
NSSO has four divisions:
 Survey Design and Research Division (SDRD)
 Field Operations Division (FOD)
 Data processing division (DPD)
 Coordination and Publication Division (CPD)
Question 6.
Calculate the standard deviation from the following data by the Actual Mean method.
Answer:
Question 6.
Write the assumptions of the Linear Regression Model?
Answer:
Assumptions of the Linear Regression Model:
The Linear regression model is based on certain assumptions
 Some of them refer to the distribution of the random variable.
 Some of them refer to the relationship between U_{i} and the explanatory variables (x_{1}, x_{2}, x_{3} given in the above example).
 Some of them refer to the relationship between U_{i} the explanatory variables themselves.
X. Answer the following questions
Question 1.
Distinguish between correlation and Regression.
Answer:
Correlation  Regression 
Correlation is the relationship between two or more variables, which vary with the other in the same or the opposite direction.  Regression means going back and it is a mathematical measure showing the average relationship between two variables. 
Both the variables X and Y are random variables.  Both the variables may be random variables. 
There may be a spurious correlation between the two variables.  In regression, there is no such spurious regression. 
It has limited application because it is confined only to linear relationships between the variables.  It has wider application, as it studies linear and nonlinear relationship between the variables. 
It is not very useful for further mathematical treatment.  It is widely used for further mathematical treatment. 
Question 2.
Explain the difference between correlation and regression?
Answer:
Difference between Correlation and Regression:
Correlation:
 Correlation is the relationship between two or more variables, which vary with the other in the same or the opposite direction.
 Both the variables X and Y are random variables.
 It finds out the degree of relationship between two variables and not the cause and effect relationship.
 It is used for testing and verifying the relation between two variables and gives limited information.
 The coefficient of correlation is a relative measure. The range of relationships lies between 1 and +1.
 There may be a spurious correlation between the two variables.
 It has limited application because it is confined only to a linear relationship between the variables.
 It is not very useful for further mathematical treatment.
Regression:
 Regression means going back and it is a mathematical measure showing the average relationship between two variables.
 Both the variables may be random variables.
 It indicates the cause and effect relationship between the variables and establishes the functional relationship.
 Besides verification, it is used for the prediction of one value, in relation to the other given value.
 The regression coefficient is an absolute figure. If we know the value of the independent variable, we can find the value of the dependent variable.
 In regression, there is no such spurious regression.
 It has wider application, as it studies the linear and nonlinear relationships between the variables.
 It is widely used for further mathematical treatment.
Question 3.
Find the coefficient of correlation with the actual mean Method for the following data:
Answer:
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 Samacheer Kalvi 12th Economics Chapter 12 Introduction to Statistical Methods and Econometrics Notes PDF Download: Tamil Nadu STD 12th Economics Chapter 12 Introduction to Statistical Methods and Econometrics Notes
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