B.Sc. (Data Science) Statistical Methods for Data Science Syllabus - Mumbai University

This is the Fourth Year BSc Data Science Honours syllabus under NEP 2020, phased in one year at a time, from the academic year 2024-25. The University still sets the earlier Choice Based papers alongside it for ATKT candidates, so check which scheme your exam form names before you revise.

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Syllabus for Statistical Methods for Data Science

Major · Semester 7 · Fourth Year BSc Data Science Honours · 2 credits · 50 marks

Module I: Introduction to Applied Statistics

The Nature of Statistics and Inference: What is “Big Data”?, Statistical Modelling, Statistical Significance Testing and Error Rates, Simple Example of Inference Using a Coin, Statistics is for Messy Situations, Type I versus Type II Errors, Point Estimates and Confidence Intervals, Variable Types, Sample Size, Statistical Power, and Statistical Significance, The Verdict on Significance Testing, Training versus Test Data. Means, Correlations, Counts: Drawing Inferences: Computing z and Related Scores, Statistical Tests, Plotting Normal Distributions, Correlation Coefficients, Evaluating Pearson’s r for Statistical Significance, Spearman’s Rho: A Nonparametric Alternative to Pearson. Tests of Mean Differences: t-Tests for One Sample, Two Sample t-Test, Paired- Samples t-Test. Categorical Data: Binomial Test, Categorical Data Having More Than Two Possibilities. Power Analysis and Sample Size Estimation: Power for t-Tests, Power for One- Way ANOVA, Power for Correlations. Analysis of Variance: Fixed Effects, Random Effects, Mixed Models, Introducing the Analysis of Variance (ANOVA), Performing the ANOVA, Random Effects ANOVA and Mixed Models, One-Way Random Effects ANOVA

Module II: Multivariate Techniques

Regression: Simple and Multiple Linear Regression, Hierarchical Regression, How Forward Regression Works, Logistic Regression and the Generalized Linear Model, Predicting Probabilities, Multiple Logistic Regression, Training Error Rate Versus Test Error Rate Multivariate Analysis of Variance (MANOVA) and Discriminant Analysis: Multivariate Tests of Significance, Example of MANOVA, Outliers, Homogeneity of Covariance Matrices, Linear Discriminant Function Analysis, Theory of Discriminant Analysis, Predicting Group Membership, Visualizing Separation. Principal Component Analysis: Principal Component Analysis Versus Factor Analysis, Properties of Principal Components, Component Scores, How Many Components to Keep? Exploratory Factor Analysis, Common Factor Analysis Model, Factor Analysis Versus Principal Component Analysis onthe Same, Initial Eigenvalues in Factor Analysis, Rotation in Exploratory Factor Analysis, Estimation in Factor Analysis. Cluster Analysis: k-Means Cluster Analysis, Minimizing Criteria, Example of k- Means Clustering, Hierarchical Cluster Analysis, Why Clustering Is Inherently Subjective. Nonparametric Tests: Mann– Whitney U Test, Kruskal–Wallis Nonparametric Test for Paired Comparisons and Repeated 10 Text Books 1. Gupta S. C., Kapoor V. K.: Fundamentals of Mathematical Statistics; Tenth Edition.Sultan 2. Chand &Sons. (2000) 3. Johnson, R.A., Wichern, D.W.: Applied Multivariate Statistical Analysis, Prentice-Hall, New Jersey, 2002. 4. Draper, N. R. and Smith, H. (1998), Applied Regression Analysis (John Wiley), Third Edition. 11 Reference Books 1. Purohit, S. G. Gore, S.D. and Deshmukh, S.R. (2015). Statistics using R, second edition. Narosa Publishing House, New Delhi. 2. Daniel W. W.: Applied Non-Parametric Statistics, First edition Boston-Houghton Mifflin Company. 12 Internal Continuous Assessment: 50% Semester End Examination: 50% Sem – VII

Text Books

1 Gupta S. C., Kapoor V. K.: Fundamentals of Mathematical Statistics; Tenth Edition.Sultan
2 Chand &Sons. (2000)
3 Johnson, R.A., Wichern, D.W.: Applied Multivariate Statistical Analysis, Prentice-Hall, New Jersey, 2002.
4 Draper, N. R. and Smith, H. (1998), Applied Regression Analysis (John Wiley), Third Edition.
1 Purohit, S. G. Gore, S.D. and Deshmukh, S.R. (2015). Statistics using R, second edition. Narosa Publishing House, New Delhi.
2 Daniel W. W.: Applied Non-Parametric Statistics, First edition Boston-Houghton Mifflin Company.

Reproduced from the University of Mumbai syllabus for B.Sc. (Data Science) under NEP 2020. Wording is as printed in that syllabus. Module numbering is as printed there too.

The complete syllabus

This subject is cut from the University circular for its year. Open a document here if you want the whole thing rather than a single subject.

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