FURTHER MODIFICATION OF THE CENTRAL PREDICTION THEORY

PREDICTING THREE RESPONSE VARIABLES FROM ONE   EXPLANATORY VARIABLE

As you may be aware: Central Prediction (Regression) Model is a statistical model that is used for predicting a set of mean-measurements x_2m, x_3m, x_4m, …, x_nm called the mean-response variables from mean-explanatory variable x_1m.

For the relationship between the variables x₁, x₂, x₃ and x₄; the central prediction (regression) equations are related as

X_2m= k₁x_1m + c ---- (1)

X_3m = K₁x_1m + k₂x_2m  + c----- (2)

X_4m = k₁x_1m + k₂x_2m + k₃x₃ + C --- (3)

Where;

K₁ = Σx₂/2Σx₁

K₂ = [Σx₁Σx₃-Σx₁Σx₂] /Σx₁Σx₂

C=Σx₂/2n

K₃= [Σx₄/n-k₁Σx₁/n-k₂Σx₂/n-c]/Σx₃/n

Most females of various ages are mostly affected by emotional fidelity when disappointment come to their relationship and may be suffered by neurotic disorder (i.e some have unreasonable fear of being loyal to their new partners due to disappointment from their early relationships; some have unreasonable fear of being in relation again; some experience societal- withdrawal due to fidelity – anxiety etc)

The table below shows the relationship between ages of females, percentage in their relationship  and 

 percentage of those who are affected by neurotic disorder in one particular town in the year 2012.

Age  (x1)	Females in relationship (%) (×2)	Those who are disappointed (%) (x3)	Those who are affected by neurotic disorder (x4)
13	45	20	19
14	49	28	22
15	52	30	33
16	55	40	41
17	56	60	62
18	57	75	73
19	57	80	79
20	69	81	80
21	70	88	88
22	80	90	89
23	85	92	90
24	90	80	85
25	85	72	70
26	65	60	61
27	56	53	50
28	42	40	39
29	39	38	36

Use the table above to estimate the average percentage of females who are in relationship, average percentage of females who are disappointed, and average percentage of females who are affected by neurotic disorder at an average age 21.

Solution

X_2m = k_1mX_1m + c

X_2m = 1.47x21 + 30.94 = 61.81

Hence, percentage female who are in relationship in the year 2012 is 62%

X_3m= k₁x_1m +k₂x_2m + c

X_3m =1447x21- (-0.004) x 61.81 + 30.94 = 60.33

Hence, percentage of female who are disappointed in their relationship is 60%.

X_4m = k₁x_1m + k₂x_2m + k₃x_3m +c

X_4m = k₁x_1m + k₂x_2m +k3x_3m +c

X_4m = 1.47x21-0.0024x63.28 -0.00836x60.33+ 30.94

X_4m=59.82

Hence, percentage of females who are suffering neurotic disorder is 60%.



REFERENCE
Galton, Francis,(1886), 'Regression Towards Mediocrity in Heredity Stature, Volume 15.