Page 85 - Basic Statistics

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variable Y according to the change (increase or decrease) in the value of the

independent variables X. This relationship is expressed in the form of a linear
equation

E ( Y j ) =  0+  1Xj ( R1)

Where  0 is the intercept, or the value of E(Y j) when X = 0, and  1 is the slope or

rate of change in E(Y j) per unit change in X.

Observations of the response variable Y, written Y j, is assumed as a

random observation from populations of random variables with the mean of

each population given by E(Y j). The deviation of an observations Yj from its

population mean E(Y j) is expressed as a random error  j. Furthermore, linear

regression models were used modeled as follows.

Y j =  0+  1Xj +  j ( R2 )

Where,

j = Observational unit j =1, 2, . . . n

Y j = The value of the j-th observation for the variable response

Xj = The value of the j-th observation of the explanatory variables.

 j = j-th error of the model

Random error  j have zero mean and are assumed to have common

2
variance  , and each error into j mutually independent. Because the only

random elements in the model Y j =  0+  1Xj +  j is  j, then this assumption

2
imply that Y j also have common variance  , and each Y j into j mutually
independent. For the purposes of estimating of significance,  j assumed

~~* CHAPTER 5 LINEAR REGRESSION MODEL *~~