Source document. This page reproduces the syllabus this course was written to, as published — its semesters, credits and paper numbers are that document’s, not this site’s. The course itself is studied on its own, in any order.

Course Information

Title	Statistical Methods
Theory Credits	3 (3 hrs/week)
Practical Credits	1 (2 hrs/week)

Course Outcomes

1. Estimate future values using curve fitting.
2. Calculate the relationship between bivariate data.
3. Find relationships in multivariate data.
4. Forecast data using regression techniques.
5. Find associations in categorical data through attributes.

Theory — Five Units

Unit 1: Curve Fitting

Bivariate data, principle of least squares, fitting of \(k\)-th degree polynomial. Fitting of straight line, second-degree polynomial, family of exponential curves and power curve.

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Unit 2: Correlation

Meaning, types of correlation, measures of correlation — scatter diagram, Karl Pearson's coefficient, Rank correlation coefficient (with and without ties), properties. Bivariate frequency distribution, correlation coefficient for bivariate data and problems.

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Unit 3: Concurrent Deviation, Multiple & Partial Correlation

Coefficient of concurrent deviation, probable error and its properties, coefficient of determination, multiple and partial correlation coefficients (three variables only), properties and problems, intra-class correlation and correlation ratio.

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Unit 4: Regression

Concept of regression, linear and non-linear regression. Linear regression — regression lines, regression coefficients and their properties, angle between two lines of regression. Regression lines for bivariate data and simple problems. Correlation vs regression. Explained and unexplained variations.

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Unit 5: Attributes

Notations, class, order of class frequencies, ultimate class frequencies, consistency of data, conditions for consistency for 2 and 3 attributes, independence of attributes, association of attributes and its measures, relationship between association and colligation of attributes.

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Practical — List of Experiments (9)

1. Fitting of straight line by the method of least squares.
2. Fitting of parabola by the method of least squares.
3. Fitting of exponential curve of two types by the method of least squares.
4. Fitting of power curve by the method of least squares.
5. Computation of correlation coefficient and regression lines for ungrouped data.
6. Computation of correlation coefficient for bivariate frequency distribution.
7. Computation of correlation coefficient and forming regression lines for grouped data.
8. Computation of partial and multiple correlation coefficients.
9. Computation of Yule's coefficient of association and colligation.

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Text Books

1. S. C. Gupta & V. K. Kapoor — Fundamentals of Mathematical Statistics, Sultan Chand & Sons.
2. K. Rohatgi & Ehsanes Saleh — An Introduction to Probability and Statistics, John Wiley & Sons.

References

1. O. P. Gupta — Mathematical Statistics, Kedarnath Ramnath & Co.
2. P. N. Arora & S. Arora — Quantitative Aptitude Statistics — Vol II, S. Chand & Company Ltd.

Suggested Co-Curricular Activities

1. Training of students by related industrial experts.
2. Assignments including technical assignments, if any.
3. Seminars, Group Discussions, Quiz, Debates etc. on related topics.
4. Preparation of audio and videos on tools of diagrammatic and graphical representations.
5. Collection of material / figures / photos of related topics.
6. Invited lectures and presentations of stalwarts on those topics.
7. Visits / field trips of firms, research organizations etc.

Exam Blueprint (recommended)

Unit	Topic	Approx. Weightage
1	Curve Fitting	20 %
2	Correlation	20 %
3	Multiple & Partial Correlation	20 %
4	Regression	20 %
5	Attributes	20 %

Quick Reference — Key Formulae

Topic	Formula
Karl Pearson r	\(r = \dfrac{n\sum xy - \sum x\sum y}{\sqrt{(n\sum x^2 - (\sum x)^2)(n\sum y^2 - (\sum y)^2)}}\)
Spearman ρ	\(\rho = 1 - \dfrac{6\sum d^2}{n(n^2-1)}\)
Probable Error	\(0.6745(1-r^2)/\sqrt n\)
Multiple R	\(R_{1.23}^2 = (r_{12}^2 + r_{13}^2 - 2 r_{12}r_{13}r_{23})/(1 - r_{23}^2)\)
Partial r12.3	\((r_{12} - r_{13}r_{23})/\sqrt{(1-r_{13}^2)(1-r_{23}^2)}\)
Regression coefficient	\(b_{yx} = r\sigma_y/\sigma_x\); \(b_{xy} = r\sigma_x/\sigma_y\); \(r^2 = b_{yx}b_{xy}\)
Yule's Q	\(\dfrac{(AB)(\alpha\beta) - (A\beta)(\alpha B)}{(AB)(\alpha\beta) + (A\beta)(\alpha B)}\)
Yule's ω	\(\dfrac{\sqrt{(AB)(\alpha\beta)} - \sqrt{(A\beta)(\alpha B)}}{\sqrt{(AB)(\alpha\beta)} + \sqrt{(A\beta)(\alpha B)}}\)
Q-ω relation	\(Q = 2\omega/(1+\omega^2)\)