Statistics, Statistical Modelling & Data Analytics

Course Objectives :                           Why this Subject?

1. To impart basic knowledge about Statistics, visualisation and probability.
2. To impart basic knowledge about how to implement regression analysis and interpret the results.
3. To impart basic knowledge about how to describe classes of open and closed sets of R, concept of compactness Describe Metric space - Metric in Rn.
4. To impart basic knowledge about how to apply Eigen values, Eigen vectors.

Course Outcomes (CO)

• CO1 Ability to learn and understand the basic concepts about Statistics, visualisation and probability.
• CO2 Ability to implement regression analysis and interpret the results. Be able to fit a model to data and comment on the adequacy of the model
• CO3 Ability to describe classes of open and closed sets of R, concept of compactness Describe Metric space - Metric in Rn.
• CO4 Ability to impart basic knowledge about how to apply Eigen values, Eigen vectors.

UNIT-I

Statistics: Introduction & Descriptive Statistics- mean, median, mode, variance, and standard deviation. Data Visualization, Introduction to Probability Distributions. Hypothesis testing, Linear Algebra and Population Statistics, Mathematical Methods and Probability Theory, Sampling Distributions and Statistical Inference, Quantitative analysis.

UNIT-II

Statistical Modelling: Linear models, regression analysis, analysis of variance, applications in various fields. Gauss-Markov theorem; geometry of least squares, subspace formulation of linear models, orthogonal projections; regression models, factorial experiments, analysis of covariance and model formulae; regression diagnostics, residuals, influence diagnostics, transformations, Box-Cox models, model selection and model building strategies, logistic regression models; Poisson regression models.

UNIT-III

Data Analytics: Describe classes of open and closed set. Apply the concept of compactness. Describe Metric space - Metric in Rn. Use the concept of Cauchy sequence, completeness, compactness and connectedness to solve the problems.

UNIT – IV

Advanced concepts in Data Analytics: Describe vector space, subspaces, independence of vectors, basis and dimension. Describe Eigen values, Eigen vectors and related results.

Textbook(s):

1. Apostol T. M. (1974): Mathematical Analysis, Narosa Publishing House, New Delhi.
2. Malik, S.C., Arora, S. (2012): Mathematical Analysis, New Age International, New Delhi

References:

1. Pringle, R.M. and Rayner, A.(1971): Generalized Inverse of Matrices with Application to Statistics, Griffin, London
2. Peter Bruce, Andrew Bruce (2017), Practical Statistics for Data Scientists Paperback