| Course Name | Multivariate Statistics |
| Course Code | 25MAT336 |
| Program | B. Sc. in Physics, Mathematics & Computer Science (with Minor in Artificial Intelligence and Data Science) |
| Semester | Electives: Mathematics |
| Campus | Mysuru |
Multivariate Random variables and Distribution functions – Variance – covariance matrix – correlation – Bivariate normal distribution, Multivariate normal density and its properties – Definition of Wishart matrix and its properties, Mahalanobis Distance. Sampling distributions of X and S, Large sample behaviour of X and S.
Classification for two populations, classification with two multivariate normal populations
Principal components analysis, Dimensionality reduction, Factor Analysis- factor loadings using principal component analysis.
Simple Linear Regression- Properties, Least Squares Estimation of parameters, Hypothesis Tests in Simple Linear Regression, Multiple Linear Regression – Estimation of model parameters.
OBJECTIVE: To enable students to understand various multivariate data analysis tools and techniques to analyze real-world problems involving multivariate data sets.
Course Outcomes
| COs | Description |
| CO1 | To exhibit the basics of multivariate random variables and sampling distributions. |
| CO2 | To apply multivariate techniques for classification of distributions. |
| CO3 | To apply the concept of PCA and its application in clustering analysis. |
| CO4 | To gain knowledge on simple linear regression, estimation, and testing of model parameters. |
| CO5 | To gain knowledge on multiple linear and nonlinear regression and estimation of model parameters. |
| PO/PSO |
PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PO6 |
PO7 |
PO8 |
PO9 |
PO10 |
PSO1 |
PSO2 |
PSO3 |
PSO4 |
| CO | ||||||||||||||
| CO1 | 2 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 2 | – |
| CO2 | 1 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 3 | – |
| CO3 | 2 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 2 | – |
| CO4 | 1 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 3 | – |
| CO5 | 1 | – | 2 | 3 | 3 | – | 2 | – | – | – | – | 3 | 2 | – |
Text Books:
References:
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