Question

QUESTION:

a) State any two weaknesses of R² as a measure of goodness of fit of a regression model

b) In the context of a linear regression model , give two examples of hypotheses that cannot be tested using either an F-Test or a t-Test

c)State any three methods that can be used to estimate the parameters of a linear regression model

d)In what ways does a population regression function differ from a sample regression function?

e)Explain three important implications of cointegration among sets of no-stationary time series

f) Distinguish between the short run and long run dynamics in a VECM

Answer 1

1. Weaknesses of r2:

• It can’t be used to find if coefficient estimates are biased. As a result of which it is necessary to assess the residual plots.
• It doesn’t indicate whether a given regression model is an appropriate fit for the data.

1. No information about this in any of the sources.
2. Any three methods for estimating the parameters:

• Simple linear regression – least square method.

This method estimates the parameters of the model base on observed pairs of values & applying certain criterion function.

• Multiple linear regressions – least squares method.

This method estimates the parameters based on observed n sets of values & applying certain criterion function.

• Non linear model – method of Gauss – Newton-least squares method:

This method estimates the parameters of the model based on n observed pairs of values & applying certain criterion function.

1. POPULATION & SAMPLE REGRESSION FUNCION:

A population regression function is defined as a regression function in which it hypothesizes a theoretical relationship between a dependent & set of independent or explanatory variables at population level.

A stochastic error is available in the model which is written as :

y = b0 +b1x+u

Where y = dependent variable

X = explanatory variable

U = stochastic error term

B0 = intercept term

B1 = slope coefficient

It is stated how population mean variable is related with one or more explanatory variables.

Sample regression function:

This is the sample counterpart of population regression function. Different samples generate different estimates as SRF is arrived for a given sample.

It is written as:

y = b0+b1x+e

These are considered to fitted values of population estimators, where for each value of x, there is fitted value of y & e is the residual error term.

1. Implications of co integration:

• Co integration is used to tests & estimate relations between non stationary variables such as consumption & incomes, interest rates at different maturities & stock prices.
• The co integration is used to deal with difficulties that arise when using non stationery series that has long run equilibrium relationship.
• When data is no stationery, it can be bought back to stationery by linear transformation of differencing.

1. Short & long run equilibrium:

Short run:

The main focus is on the matrices alpha & beta. Interpreting them includes the same difficulties as VAR analysis especially when there are many variables.

Structural equation modeling (SEM) CAN ALSO BE APPLIED TO CONINTEGRATION FRAMEWORK.

Long run:

As most of the time series is non stationery, using regression analysis gives unreliable estimates for which it is necessary to make the series stationery of the same order, is it is not integrated at the same level, long run estimation is used.