Sudarshan Kumar Patel 1320

Koushik Kanti Das 1309

Introduction

Method

Application

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.

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.

• Generalization of the univariate normal

• Determined by the mean (vector) and covariance matrix

• E.g. Standard bivariate normal

Example – Crime Rates by State

Obs State Murder Rape Robbery Assault Burglary Larceny Auto_Theft

1 Alabama 14.2 25.2 96.8 278.3 1135.5 1881.9 280.7

2 Alaska 10.8 51.6 96.8 284.0 1331.7 3369.8 753.3

3 Arizona 9.5 34.2 138.2 312.3 2346.1 4467.4 439.5

4 Arkansas 8.8 27.6 83.2 203.4 972.6 1862.1 183.4

5 California 11.5 49.4 287.0 358.0 2139.4 3499.8 663.5

… … ... ... ... ... ... ... ...

Crime Rates per 100,000 Populations by State

Simple Statistics

Murder Rape Robbery Assault Burglary Larceny

Auto

Theft

Mean 7.444000000 25.73400000 124.0920000 211.3000000 1291.904000 2671.288000377.526

0000

SD 3.866768941 10.75962995 88.3485672 100.2530492 432.455711 725.908707193.394

4175

Observations 50

Variables 7

The PRINCOMP Procedure

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

The simple linear regression MODEL is:

y = β0 + β1x +ε

describes how y is related to x

β0 and β1 are called parameters of the model.

ε is a random variable called the error term.

Graph of the regression equation is a straight line.

β0 is the population y-intercept of the regression line.

β1 is the population slope of the regression line.

E(y) is the expected value of y for a given x value

Regression

Models

LinearNon-

Linear

2+ ExplanatoryVariables

Simple

Non-Linear

Multiple

Linear

1 ExplanatoryVariable

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.

The graph above shows the production trend of chana and pulses which depends on the above

mentioned factors.