Page 94 - Basic Statistics

89

ˆ
ˆ
a. The calculation of the value of the coefficient β and β :
1
0
ˆ
2
β = ( Xj - X )( Y j - Y ) /  (Xj - X )
1
ˆ
β = [  X j Y j – (  X j )(  Y j) / n ] / [  X j - (  X j ) / n ]
2
2
1
= [1991.303 – (348.8)( 68.37) / 12 ] / [10156.66 - (348.8) / 12 ]
2
= 0.2205

ˆ
ˆ
β = Y - β X
1
0
= 5.6975 – 0.2205 ( 29.07 )
= -0.7124

ˆ
The allegation regression equation Y = -0.7128 + 0.2205 Xj
j

b. Hypotheses:

H 0 :  1 = 0.

H 1 :  1  0

The calculation of the sum of squares:

SS(Total) =  Y j – (  Y j ) / n
2
2
= ( 390.8075 ) – ( 68.37 ) / 12
2
2
= 1.2694

ˆ 2
SS(Reg) = β [  X i - (  X i ) / n ]
2
2
1
= (0.2205) ( 10156.66 – (348.8) / 12 )
2
2
= 0.8854
RSS(Reg) = 0.8854 / 1

= 0.8854

SS(Res) = SS(Total) – SS(Reg)

= 1.2694 – 0.8854

~~* CHAPTER 5 LINEAR REGRESSION MODEL *~~