3. 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.
4. 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.
5. • 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
7. 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
8. 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
9. Regression
Models
Linear
Non-
Linear
2+ Explanatory
Variables
Simple
Non-
Linear
Multiple
Linear
1 Explanatory
Variable
10. 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.
