Multivariate analysis

1. Sudarshan Kumar Patel 1320 Koushik Kanti Das 1309 Multivariate Analysis

2. Multivariate analysis (MVA) is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical outcome variable at a time . Components- The Variate Measurement scales Measurement error and multivariate measurement. Statistical significance Vs Statistical power Variate value = w1x1 + w2x2 + ...+ wnxn x1 ,x2 ,..xn = Observed variable w1 , w2 ,.. wn = Weight The variables are specified by the researcher. The weights are determined by the multivariate technique. Introduction

3. Cross correlations: - An important exploratory tool for modeling multivariate time series is the cross correlation function (CCF). The CCF generalizes the ACF to the multivariate case. Thus, its main purpose is to find linear dynamic relationships in time series data that have been generated from stationary processes.   Single-equation models: - Two types of so-called single-equation models can be considered for multivariate forecasting: regression models and transfer-function models.   Vector auto regressions and VARMA models Cointegration: - Although VAR modeling traditionally assumes stationary of all series, it is not generally recommended to difference non-stationary components individually, as such a step may destroy important dynamic information. Types of Multivariate Models

4. • Generalization of the univariate normal • Determined by the mean (vector) and covariance matrix • E.g. Standard bivariate normal Example – Crime Rates by State Multivariate Normal Distribution Crime Rates per 100,000 Populations by State

5. Contt ………. Simple Statistics   Murder Rape Robbery Assault Burglary Larceny Auto Theft Mean 7.444000000 25.73400000 124.0920000 211.3000000 1291.904000 2671.288000 377.5260000 SD 3.866768941 10.75962995 88.3485672 100.2530492 432.455711 725.908707 193.3944175 Observations 50 Variables 7 The PRINCOMP Procedure

6. Application Consumer and market research Quality control and quality assurance across a range of industries such as food and beverage, paint, pharmaceuticals, chemicals, energy, telecommunications, etc Process optimization and process control Research and development

7. The simple linear regression MODEL is: y = β + β 1 x + ε describes how y is related to x β and β 1 are called parameters of the model. ε is a random variable called the error term . Graph of the regression equation is a straight line. β is the population y- intercept of the regression line. β 1 is the population slope of the regression line. E ( y ) is the expected value of y for a given x value Simple Regression

8. There are several variables that affect crop production. These variables may be static or dynamic. The static variables include soil properties; seed variety etc. and the dynamic variables include temperature, rainfall, humidity, sunshine hours, technology, demand etc. Application in agriculture