Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Bootstrapping (statistics) wikipedia , lookup
Taylor's law wikipedia , lookup
Gibbs sampling wikipedia , lookup
Time series wikipedia , lookup
Foundations of statistics wikipedia , lookup
Resampling (statistics) wikipedia , lookup
Statistical inference wikipedia , lookup
Syllabus for P.G. Diploma in Statistics under CBCS Department of Statistics North-Eastern Hill University P.G. Diploma in Statistics (Choice Based Credit System) Department of Statistics, NEHU Duration of the Course: Two Semester (Full Time) Credit structure MAXIMUM MARKS: 900 • No. of credit: 36 • Core credits: 30 • Open choice: 6 Credit: • 1 credit = 25 marks. • 4 credit = 100 marks. Eligibility for admission: Any one who has passed the B.A/B.Sc/B.Com examination of this University or any other University with Mathematics as a subject at 10+2 level. First semester Second semester STA C 101(D) Descriptive Statistics: 4 credits STA C 201(D) Statistical Inference: 4 credits STA C 102(D) Numerical Analysis and Elements of Probability Theory: 3 credits STA C 202(D) Sample Survey Methodology: 2 credits STA C 103(D) Distribution Theory: 3 credits STA C 203(D) Analysis of Variance and Design of Experiments: 2 credits STA C 104(D) Practical 1: 2 credits STA C 204(D) Economic Statistics: 2 credits STA C 105(D) Practical 2: 2 credits STA C 205(D) Linear Algebra: 2 credits STA O 106(D) Mathematics : 2 credits (open) STA C 206(D) Practical 1: 2 credits STA O 107(D) Vital and Official Statistics: 2 credits (open) STA C 207(D) Practical 2: 2 credits * * STA O 108(D) Biometry : 2 credits (open) STA O 208(D) Linear Programming: 2 credits (open) * STA O 209(D) Introduction to Econometrics: 2 credits (open) Total Credits: 36 * Courses offered under the Master’s programme of the Department [1] 1. 1 credit is assigned for each 25 marks and 12 contact hours of teaching for theory or 24 contact hours of teaching for practical. 2. For each course, 25 % marks are to be allotted for internal assessment 3. A minimum of 10 practicals to be done in each practical course of 2 credits. 4. For Open Courses, practical classes/questions are to be included in theory classes/questions. 5. For all theory courses, two questions are to be set from each unit and one question to be attempted. 6. For all practical courses, which are of 50 marks (2 credits) three questions of 15 marks to be set from the list of practicals and two to be attempted. 7.5 marks for the viva voce. 7. At most two open courses in first semester and at most one open course in second semester can be taken. [2] SEMESTER I STA C 101(D): Descriptive Statistics 4 credits Unit 1: Meaning of Statistics. Primary and secondary data. Collection of data and scrutiny of data, Frequency and non – frequency data. Tabular and diagrammatic representation of non – frequency data (line diagram. Ratio chart, bar diagram, pictograph and pie diagram). Tabular representation of frequency data: Frequency, relative frequency, cumulative frequency and frequency density. Column diagram, frequency polygon, histogram and cumulative frequency diagram. (10 Lectures) Unit 2: Central tendency and dispersion. Measures of central tendency: mean, median and mode. Measures of dispersion: range, mean deviation and standard deviation, coefficient of variation and coefficient of concentration. Moments and quantiles, skewness and kurtosis of a frequency distribution. (15 Lectures) Unit 3: Bivariate data, scatter diagram, concept of correlation and correlation coefficient. Simple regression by least-squares method: its relationship with simple correlation. Correlation ratio. Rank correlation: Spearman’s and Kendall’s coefficients. Theory of attributes. (13 Lectures) Unit 4: Multivariate data, multiple regression by least squares method ( up to two independent variables), multiple and partial correlation coefficients. (10 Lectures) Text Books: Bhattacharya, G.K. and Johnson, R.A. (1977) : Statistical Concepts and methods : Wiley Eastern, New Delhi. Hangal, David D. (2009), Introduction to Applied Statistics : A Non Calculus Based Approach, Narosa Publishing House, New Delhi. Hooda, R.P. (2002). Introduction to Statistics, Macmillan Publishers India Ltd., New Delhi. Shenoy, G.V. (2000). Statistical Methods in Buisness and Social Science. Macmillan Publishers India Ltd., New Delhi. Goon, A.M., Gupta, M.K. and Das Gupta, B (1985) : Basic Statistics (for students of economics, Commerce, accountancy and the biological sciences), World Press, Kolkata. Gun, A.M., Gupta, M.K. and Das Gupta, B (2008) :Fundamentals of Statistics, Vol.I, World Press, Kolkata. [3] STA C 102(D) Numerical Analysis and Elements of Probability Theory 3 credits Unit 1: Numerical analysis : Approximate numbers ; rounding off, significant figures, digits, errors of approximation. Finite differences, interpolation, Newton’s Gregory formula for forward and backward interpolation. Divided difference formulae Inverse interpolation, numerical solution in one unknown – iterative methods. Numerical differentiation: Newton’s backward, forward and Lagrange’s interpolation. Numerical integration: Trapezoidal rule, Simpson’s one third rule. Summation of series – Euler Meclaurin formula. Stirling’s approximation of factorials (without proof). (12 Lectures) Unit 2: Experiments and Events Randomness and Statistical regularity. Classical definition and its limitation, Relative frequency, subjective and axiomatic approach to probability . Basic results on probability, law of large numbers, central limit theorem (statements) (12 Lectures) UNIT 3: Conditional probability, theorem of compound probability and total probability. Independence of events. Independent trials. Problems on probability involving the basic theorem. Bayes theorem. (12 Lectures) Text Books Mukhopadhyay, P.(2002). Theory of Probability. New Central Book Agency (P) Ltd. Kolkata Ross, S.M. (2004), Introduction to probability and Statistics for Engineers and Scientists, Elsevier Academic Press, USA. Chandra, T.K. and Chatterjee, D.(2003). A First Course in Probability, Second Edition. Narosa Publishing House, New Delhi. Scarborough, J. B. (1966) Numerical Mathematical Analysis, (sixth edition), Oxford and IBH Publishing Co., New Delhi. Demidovich, B.P. and Maron, I.A., (1981) Computational Mathematics, Mir Publishers, Moscow [4] STA C 103(D) Distribution Theory 3 credits Unit 1: Random Variables – Concept, Discrete, Continuous and Mixed. Probability Functions and Distribution Functions. Expectation and Variance. Sum and Product Laws of Expectation. Independency of Random Variables. Joint Distribution of Random Variables, Marginal and Conditional Distributions. Transformation of Two-Dimensional Random Variables. (12 Lectures) Unit 2: Discrete Probability Distributions – Uniform, Hypergeometric, Negative Binomial Distribution. Binomial, Poisson, Geometric, (12 Lectures) Unit 3: Continuous Probability Distributions – Rectangular, Gamma, Beta (Fist and Second Kinds), Normal, Log-Normal, Exponential and Bivariate Normal. (12 Lectures) Text Books: Cooper, R. A. and Weekes, A. J. (1983), Data, Models and Statistical Analysis, Heritage Publishers, New Delhi Chao, L. L. (1974), Statistical Methods and Analysis, McGraw Hill Book Company, New York Gupta, S. C. and Kapoor, V. K. (2006), Fundamentals of Mathematical Statistics, Sultan Chand and Sons, New Delhi. Hogg, R.V. and Craig, A.T. (2002). Introduction to Mathematical statistics, Pearson Education, Delhi. [5] STA C 104(D) Practical 1 2 credits 1. Plotting of Frequency Distribution : line, bar, pie, frequency polygon 2. Plotting Histogram 3. Computation of mean, median and mode for ungrouped and grouped frequency distrbution 4. Computation of variance,standard deviation,mean deviation 5. Computing coefficient of variation and coefficient of concentration 6. Moments, quartiles, skewness and kurtosis of frequency distribution 7. Calculating correlation coefficient from ungrouped and grouped data 8. Fitting a straight line by least square method 9. Computing rank correlation 10. Problems on association of attributes 11. Computing partial and multiple correlation coefficient 12. Fitting a linear regression of Y on X1 and X2 Text Books: Hooda, R.P. (2002). Introduction to Statistics, Macmillan Publishers India Ltd., New Delhi. Shenoy, G.V. (2000). Statistical Methods in Buisness and Social Science. Macmillan Publishers India Ltd., New Delhi. Goon, A.M., Gupta, M.K. and Das Gupta, B (1985) : Basic Ststiatics (for students of economics, Commerce, accountancy and the biological sciences), World Press, Kolkata. Gun, A.M., Gupta, M.K. and Das Gupta, B (2008) :Fundamentals of Statistics, Vol.I, World Press, Kolkata. [6] STA C 105(D) Practical 2 2 credits 1. Fitting of Binomial Distribution 2. Fitting of Poisson Distribution 3. Fitting of Normal Distribution 4. Fitting of Negative Binomial Distribution 5. Fitting of Log-Normal Distribution 6. Difference table: location and correction of error 7. Interpolation by Newton’s forward, backward and Lagrange’s formula 8. Inverse interpolation 9. Numerical solutions of equations in one unknown by iterative methods 10. Numerical differentiation using Newton’s and Lagrange’s interpolation formula 11. Numerical Integration by trapezoidal and Simpson’s 1/3 rule 12. Use of Euler – Maclaurin formula for summation of series and numerical integration. Text Books: Chao, L. L. (1974), Statistical Methods and Analysis, McGraw Hill Book Company, New York Gupta, S. C. and Kapoor, V. K. (2006), Fundamentals of Mathematical Statistics, Sultan Chand and Sons, New Delhi Scarborough, J. B. (1966) Numerical Mathematical Analysis, (sixth edition), Oxford and IBH Publishing Co., New Delhi. [7] STA 0 106(D) Mathematics 2 credits (open) Unit I: Real valued functions and their graphs. Limits of algebraic and trigonometric functions, standard limits based an logarithmic and exponential functions (without proof, application only). Continuity and differentiability of exponential, logarithmic and trigonometric functions. Derivatives ; sum, product and quotient rule, chain rule, differentiation of implicit and parametric forms. Maxima, Minima, Mean Value theorem. Rolle’s theorem. (12 Lectures) Unit 2: Indefinite integral as inverse process of differentiation. Methods of integration: substitution method, partial fraction and integration by parts. Fundamental theorem of calculus, evaluation and properties of definite integrals, Applications of definite integrals. Definite integrals expressed as the limit of the sum. Area under curves. Differential Equation: Basic concepts. General and particular solution, Formation of differential equations. Equations of first order and first degree. (12 Lectures) Text Books Lang, S.(2006). A First Course in Calculus, Fifth Edition, Springer. Apostol, T. M.(2006). Calculus, Volume I, Second Edition, Wiley India Edition. Thomas and Finney :(2008). Calculus and Analytic Geometry , Narosa Publications, New Delhi [8] STA O 107(D) Vital and Official Statistics 2 credits (open) Unit 1: Vital Statistics: Concept of Demography and population Sciences, Measures of Mortality – Crude, Specific and Standardized Death Rates, Comparative Mortality Index and Maternal Mortality Rate. Measures of Fertility – Crude birth, General Fertility, Specific Fertility, Total Fertility, Gross Reproduction and Net Reproduction Rates. Computation of Rate of Population Growth – Arithmetic, Geometric and Exponential. Description of a complete Life table. (12 Lectures) Unit 2: Official Statistics: Role of DSO, NSSO, Office of Registrar-General and State Statistical Bureaus. Evaluation of Family Planning Programmes – Concept and definition. Evaluation of Fertility Impact of Family Planning Programmes – Introduction and Basic Concepts only. (12 Lectures) Text Books: Gupta, S. C. and Kapoor, V. K. (2006), Fundamentals of Applied Statistics, Sultan Chand and Sons, New Delhi Gun, A. M., Gupta, M. K. and Dasgupta, B. (2008), Fundamental of Statistics Volume II. The World Press, Kolkata [9] STA O 108(D) Biometry 2 credits (open) Unit 1 An introduction to Biometry and Statistics : data collection and data presentation, frequency distribution, graphical representation, measures of central tendency, dispersion, skewness and kurtosis. Probability distribution : Binomial, Poisson and Normal distribution. (6 Lectures) Unit 2 Introduction to bivariate frequency data and its measurement : covariance, correlation, scatter diagram. Regression analysis : Linear regression, regression coefficient, fitting of regression equation by least square method. (7 Lectures) Unit 3 Population, sample. Statistic, standard error, estimation, confidence interval and confidence level, confidence interval estimate of proportion and mean. Hypothesis and its types, errors, level of significance. Test statistics : Student’s Chi-square, F and ZStatistics and their applications in testing of hypothesis. (7 Lectures) Unit 4 An introduction to Analysis of Variance (ANOVA),its definition, assumptions and uses. One way classification and statistical analysis of the model involved in it. (4 Lectures) Text Books Hogg, R. V. & Tanis, E. A. (2002): Probability and Statistical Inference Pearson Education, Asia. Mood, A. M., Graybill, F. A. and Boes D. C (1999): Introduction to the theory of Statistics. McGraw –Hill, New York. Additional Reference Arora, P. N and Malhan, P. K (2001): Biostatistics, Himalaya Publishing House, New Delhi. Goon, A. M., Gupta, M. K. and Das Gupta, B. (2006): Basic Statistics, World Publication, Kolkata. [10] SEMESTER II STA C 201(D) Statistical Inference 4 credits Unit 1: Statistic and parameter. Random sampling from a distribution. Sampling distribution of a statistic and its standard error under random sampling. Sampling distributions of the sample sum in sampling from a binomial and Poisson distribution. Sampling distribution of sample mean and sample variance in sampling from a univariate normal distribution. Definitions of chi-square, t and F statistics and their probability density functions and basic properties (without derivations). (14 Lectures) Unit 2: Point and interval estimation. Intuitive considerations underlying the principles of unbiasedness, minimum variance and consistency. Basic principles of hypothesis testing: test, critical region, type I error and type II error, level of significance and power of a test. (12 Lectures) Unit 3: Tests for a single mean, for the equality of two means, for a single variance and for the equality of two variances, for the significance of correlation coefficient (under normal population models). (8 Lectures) Unit 4: Large-sample tests: for binomial proportion and for the equality of two binomial proportions, for a single mean and for difference of means of two independent populations and related confidence intervals. Pearsonian chi-square and its application in testing for goodness of fit, for independence and for homogencity. Yates’ correction for continuity in 2 x 2 table. (12 Lectures) Text Books Casella. G and Berger R.L. (1990) Statistical Inference, Wordsworth and Brooks, California. Hogg, R.V. and Craig, A.T. (2002). Introduction to Mathematical statistics, Pearson Education, Delhi. Kale, B.K. (1999). A First Course on Parametric Inferences, Narosa Publishing House, New Delhi. Rohatgi V. (1998). An Introduction to Probability and Mathematical Statistics. Wiley Eastern. [11] STA C 202(D) Sample Survey Methodology 2 credits UNIT 1: Complete enumeration survey and sample survey and their relationship. Need for sampling. Sampling and Non-sampling errors. Basic concepts : Unit, population and parameters. Sampling unit and sampling frame. Random sample and sampling design. Sample estimators and their properties. Measures of error – Mean Square Error (MSE) and Standard Error (SE). Sampling and cost efficiency. Interpenetrating sub samples (IPNSS) Basic Sampling Techniques : Simple random sampling with and without replacement (SRSWR & SRSWOR) – point and interval estimation of population mean/total and proportion, determination of sample size. (7 lectures) UNIT 2: Basic Sampling Techniques (Continued) : Linear (LSS) and Circular (CSS) systematic sampling, Unbiased variance estimation – use of IPNSS. Probability proportional to size with replacement (PPSWR) sampling. Sample selection – cumulative total and Lahiri’s methods. Estimation of population total/mean and unbiased variance estimation. Stratified sampling, allocation problem. (9 lectures) UNIT 3: Ratio, difference and regression methods of estimation under SRS only. Non-sampling error – dealing with non response error. Planning and execution of sample surveys, methods of data collection – questionnaire vs schedule. Problems of sampling frame, choice of sampling design, pilot survey, field work etc. NSSO rounds – sampling design and field operations. (8 lectures) Text Books Cochran, W.G. (1997) : Sampling Techniques, Wiley Eastern, New Delhi. Murthy, M.N. (1967) : Sampling Theory and Methods, Statistical Publishing Society, Kolkata. Sukhatme, P.V., Sukhatme, B.V. Sukhatme, S. and Asok, C. (1984) : Sampling Theory of Surveys with Applications, Indian Society of Agricultural Statistics, C/o IASRI, Library Avenue, New Delhi. Additional Books Mukhopadhyay, P. (1998) : Theory and Methods of Survey Sampling, Prentice Hall of India, New Delhi. Raj, D and Chandhok, P. (1998) : Sample Survey Theory, Narosa Publishing House, New Delhi. Sampath, S. (2001) : Sampling Theory and Methods, Second Edition, Narosa Publishing House, New Delhi. [12] STA C 203(D) Analysis of Variance and Design of Experiments 2 credits Unit 1: Analysis of variance: Analysis of data for a one-way classification : fixed effects and random-effects models. Analysis of data for a two way classification with the same number of observations per cell : main effects and interaction effects for fixed-effects model only and estimation of error variance. (12 Lectures) Unit 2: Design of Experiment: Controlled experiments. Basic principles of designs: randomization, replication and local control. Description and method of analysis of experiments conducted according to a completely randomized, a randomized block and a latin square design. 2 3 Factorial experiments: 2 and 2 experiments. Confounding: complete and partial. (12 Lectures) Text Books: Searle, S. R. (1971). Linear Models. Wiley, New York. Cochran, W.G. and Cox, G.M. (1959). Experimental Designs, Asia Publishing House, Singapore. Montgomery, C.D. (2001). Design and Analysis of Experiments, John Wiley, New York. Gun, A.M., Gupta, M.K. and Das Gupta, B (2008) :Fundamentals of Statistics, Vol.II, World Press, Kolkata. [13] STA C 204(D) Economic Statistics 2 credits Unit 1: Time Series: Introduction, Components. Measurement of Trend – Graphic Method, Method of Semi-Averages, Method of Moving Averages and Method of Curve fitting by the Principle of Least Squares (Straight line, Second Degree Polynomial & Exponential Curve) and Spencer’s 15-point Formula. Measurement of Seasonal Fluctuations – Method of Simple Averages, Ratio to Trend method, Ratio to Moving average and Link Relative Method. Measurement of Cyclic Fluctuation. Autocorrelation and Correlelogram (Concept only). (12 Lectures) Unit 2: Index Number: Introduction, Problem Involved in its Construction, Calculation of Index Numbers, Criteria of Good Index Numbers, Classification of Index Numbers, Cost of Living Index Number and its Construction. Base Shifting, Splicing & Deflating of Index Numbers. Demand Analysis: Laws of Supply and Demand, Price Elasticity of Demand & Supply, Pareto Law of Income Distribution. (12 Lectures) Text Books: Cooper, R. A. and Weekes, A. J. (1983), Data, Models and Statistical Analysis, Heritage Publishers, New Delhi Chao, L. L. (1974), Statistical Methods and Analysis, McGraw Hill Book Company, New York Gupta, S. C. and Kapoor, V. K. (2006), Fundamentals of Applied Statistics, Sultan Chand and Sons, New Delhi Gun, A. M., Gupta, M. K. and Dasgupta, B. (2008), Fundamental of Statistics Volume II. The World Press, Kolkata [14] STA C 205(D) Linear Algebra 2 credits Unit 1: Linear equations and matrices, square matrix, equality of matrices, Addition, scalar multiplication, product of matrices, transpose, conjugate transpose, Inverse of a matrix, nilpotent, idempotent, symmetric and skew symmetric matrices: row vectors and column vectors of a matrix. Linear independence of row/column vectors. (12 Lectures) Unit 2: Rank and basis of a set of vectors, rank of a matrix, determination of rank by elementary operations. Determinants, properties of determinant. Adjoint of a matrix, inverse ; determinental rank of matrix, system of linear equations ; Homogeneous and nonhomogeneous, Cramer’s rule. (12 Lectures) Text Books: Kolman, B. and Hill, B.R.Lay, David C. (1997) Linear Algebra and its Applications, Addison Wesley. Hadley, G. (2002) Linear Algebra, Narosa Publishing House, New Delhi. Mittal, R.K. & Shanti Nararyan.(2008): Matrices, S. Chand, New Delhi. [15] STA C 206(D) Practical 1 2 credits 1. Large Sample Tests for mean and proportion 2. Large Sample Tests for Equalities of means and proportions 3. Exact Test for Sample Correlation Coefficient 4. Tests for equality of means and variances for small samples 5. Test of goodness of fit 6. Test of independence of attributes in Contingency table 7. Analysis of Variance for One-way classification 8. Two-way classification (one observation per cell) 9. Analysis of CRD, RBD and LSD 2 3 10. Analysis of 2 and 2 experiments 11. Computation of Index numbers 12. Computation of Trend by Curve Fitting (Straight Line) and Moving Averages 13. Computation of Seasonal Fluctuation by Link Relative Method Text Books Casella. G and Berger R.L. (1990) Statistical Inference, Wordsworth and Brooks, California. Hogg, R.V. and Craig, A.T. (2002). Introduction to Mathematical statistics, Pearson Education, Delhi. Rohatgi V. (1998). An Introduction to Probability and Mathematical Statistics. Wiley Eastern. Gupta, S. C. and Kapoor, V. K. (2006), Fundamentals of Applied Statistics, Sultan Chand and Sons, New Delhi Gun, A. M., Gupta, M. K. and Dasgupta, B. (2008), Fundamental of Statistics Volume II. The World Press, Kolkata Montgomery, C.D. (2001). Design and Analysis of Experiments, John Wiley, New York. [16] STA C 207(D) Practical 2 2 credits 1. Evaluation of determinant by pivotal condensation method. 2. Matrix Inversion – Gaussian method 3. Solution of simultaneous linear equations by Cramer’s Rule 4. SRSWR – all possible samples – demonstration of unbiasedness or otherwise of Estimators 5. SRSWOR – all possible samples – demonstration of unbiasedness or otherwise of Estimators 6. SRSWR – sample selection and point and interval estimation of population total/mean along its s.e. 7. SRSWOR – sample selection and point and interval estimation of population total/mean along its s.e. 8. Estimation of population proportion in SRSWR and SRSWOR. 9. LSS – all possible samples and estimation of population mean/total verification of estimators. 10. PPSWR – selection of samples and estimation of parameters. 11. Stratified sampling – estimation 12. Stratified sampling – allocation of sampling to strata Text Books Murthy, M.N. (1967) : Sampling Theory and Methods, Statistical Publishing Society, Kolkata. Singh, D and Chaudhury (1996) : Theory and Analysis of Sample Survey Designs, New Age International Ltd. New Delhi/Guwahati. Kolman, B. and Hill, B.R.Lay, David C. (1997) Linear Algebra and its Applications, Addison Wesley. Hadley, G. (2002) Linear Algebra, Narosa Publishing House, New Delhi. Mittal, R.K. & Shanti Nararyan.(2008): Matrices, S. Chand, New Delhi. [17] STA O 208(D) Linear Programming 2 credits (open) Unit 1 Introduction to Linear Programming (LP). Mathematical Formulation of Linear Programming Problem (LPP). Graphical solution to LPP. (4 Lectures) Unit 2 General LPP, Canonical and Standard forms of General LPP, Duality in LPP , Simplex Method. Big-M method and Two-phase method. (14 Lectures) Unit 3 Transportation and Assignment problems. (Including Traveling Salesman’s Problem). (6 Lectures) Text Book Gass, S. I. (1975) Linear Programming: Method and Application, Mc Graw – Hill, New York. Shevoy, G. V. (1992), Linear Programming: Methods and Applications, Wiley Eastern, New Delhi. [18] STA O 209(D) Introduction to Econometrics 2 credits (open) Unit 1 Nature of econometrics. The general linear model (GLM) and its extension. Ordinary least squares (OLS) estimation and prediction. Use of dummy variables and seasonal adjustment. Generalized least squares (GLS) estimation and prediction. Heteroscedastic disturbances. Pure and mixed estimation. Grouping of observations and of equations. (8 Lectures) Unit 2 Auto correlation, its consequences and tests. Theil BLUS procedure. Estimation and prediction. Multicollinearity problems, its implications and tools for handling the problem. Ridge regression. (8 Lectures) Unit 3 Linear regression with stochastic regressors. Instrumental variable estimation. Errors in variables. Autoregressive linear regression. Distributed lag models. Use of principal components, canonical correlations and discriminant analyses in econometrics. (8 Lectures) Text Books Apte PG (1990). Test book of Econometrics, Tata McGraw Hill, New Delhi. Johnston, J. (1984). Econometric methods, McGraw Hill, New York. Ray, Devraj (1998). Development Economics, Oxford University Press, Oxford. Additional References CSO (1980). National Accounts Statistics – Sources and Health, New Delhi. Intrulligator, M.D. (1980). Econometric models-Techniques and Applications, Prentice Hall of India, New Delhi. Nagar, A.L. (1983). Basic Statistics, Oxford University Press, Oxford. [19]