PRESENTATION DAY OF MY THEORY IN UDS

THE CENTRAL POINT THEORY AND  ITS EFFECTS ON PREDICTIVE THEORY

WILLIAM AYINE ADONGO

FAS/0912/06

OPTION:ACTUARIAL SCIENCE

ABSTRACT
     ●OBJECTIVES
           ●METHODOLOGY

●RESULTS
                 ●CONCLUSION AND              RECOMMENDATION

The Objective
The topic of the project attempts to determine the meaning of Central Point Theory; the effects of the Central Point Theory in predictive models; and as whether the availability of the Central Point Theory affect positively in prediction models.

The Methodology
Here, the Central Point Theory is practically applied in prediction modeling that hypothesized the exact relation between variables that predict several mean response variables from only  one mean explanatory variable that provide no room for random error(except complicated cases). The model in two variables is explained as:

X_2m=β₀+β₁x_1m
X_2m=mean dependent or mean response variable
X_1m=mean independent or mean predictor variable
β₀(beta zero)=constant=∑x₂/2n
β₁(beta one)=predictive coefficient=∑x₂/2∑x₁

The study found that the Central Prediction theory can be applied in the data type like binary, categorical, ordinal, binomial, count, real-value(additive),and real-value(multiplicative).The model used to analyze the fertility rate of a country which defined as the number of children a woman citizen bears, on average, in her life time.

Scientific American (December.1993) reported on the researchers found that family planning can have a great effect on fertility rate x₂, and contraceptive prevalence x₁ (measured as the percentage of married woman who use contraceptives) for each of 6 developing countries.
 

Table 1:contraceptive  prevalence  and fertility rate of  six developing country in the year 1993

COUNTRY	CONTRACEPTIVE  PREVALENCE  x1	FERTILITY RATE  x2
Ghana	14	6.0
Pakistan	13	5.0
Senegal	13	6.5
Sudan	10	4.8
Yemen	9	7.O
Nigeria	7	5.7

Step 1
We first, hypothesize a central prediction model relating average fertility rate, x_2m, to average
contraceptive prevalence, x_2m’
 
x_2m =β₀+β₁x_1m

Step 2
We estimate the predictive coefficient β₁ and the constant  β₀. Hence, we have
 
β₁= 0.330
 
β₀ = 2.917

and the central prediction equation is
 
x_2m = 2.917+ 0.330x_1m

Step 3
Using the fitted central prediction equations to estimate the exact average fertility rate of the

developing countries in December 1994, if the exact average contraceptive prevalence for the

developing countries in December 1994 is 8.83%
 
x_2m= 2.917 +0.330 (8.83) =5.831

Hence the exact average fertility rate for the developing countries in December 1994 is 5.831%.

Results
 After analysis of the Central Prediction Theory in various type of data, using the binary, categorical, ordinal, binomial, count, real-value(additive) and real-value(multiplicative). The methodology clearly and precisely represents the central prediction theory better than the existing “regression theory”.

Conclusion
The central point theory which I am developing is applied in prediction models. Through the knowledge of the central point theory, I devised a predictive theory called central prediction  which can be used in analyzing binary, categorical, ordinal, binomial, count,  real-value(additive) and real-value(multiplicative) data. The central prediction model is a substitute of “regression model” with special validity than the regression model.

Recommendation
Recommendations are made to better the development of the central prediction theory for  academy research, learning and teaching.