Page 89 - Basic Statistics

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The mean of the sum of squares (MS) is the sum of squares divided by

their respective degrees of freedom. The calculation of each sum of squares with
its mean (MS) is formulated as follows

2
2
SS(Total) =  Y j – nY
=  Y j – (  Y j ) / n
2
2
MS(Total) = SS(Total)/ n-1

2
ˆ 2
SS(Reg) = β  (Xj - X )
1
ˆ 2
= β [  X i - (  X i ) / n ] ( R9 )
2
2
1
MS(Reg) = SS(Reg)/ p-1

SS(Res) = SS(Total) – SS(Reg)

MS(Res) = SS(Res)/n-p

The results of variance analysis is presented through the analysis of
variance table. a value of F is also listed in the table analysis of variance. This is

for testing purposes by using the approach of distribution F.

Table 5.1 The analysis of variance

Source of Sum of Degrees of Mean Squares
variation squares Freedom ( MS ) F
(SS ) ( Df )
Regression SS(Reg) p-1 MS(Reg) MS (Re ) g
F =
Residual SS(Res) n-p MS(Res) MS (Re ) s

Total SS(Total) n-1

In partitioning the total sum of squares, SS (Reg) represents the sum of the

squares that can be explained or controlled, and SS (Res) represents the sum of

2
2
squares unexplained. MS(Reg) estimate  +  1  (Xj - X ) , and MS(Res)
2

~~* CHAPTER 5 LINEAR REGRESSION MODEL *~~