Page 107 - Basic Statistics

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The matrix X’X is

[,1] [,2] [,3] [,4]

[1,] 30.0 5733.0 2085 354.70
[2,] 5733.0 1463179.0 411076 67085.70
[3,] 2085.0 411076.0 147243 24523.00
[4,] 354.7 67085.7 24523 4583.39

and the matrix X’Y is

[,1]

[1,] 83.840
[2,] 17097.380
[3,] 5953.470
[4,] 973.641

The inverse of the X’X matrix, i.e the matrix ( X’X ) is
-1

[,1] [,2] [,3] [,4]

[1,] 2.8559225951 6.173356e-004 -0.03535068677 -4.090973e-002
[2,] 0.0006173356 3.341412e-006 -0.00001807261 1.409908e-008
[3,] -0.0353506868 -1.807261e-005 0.00053385411 1.439104e-004
[4,] -0.0409097295 1.409908e-008 0.00014391044 2.613921e-003

Estimate of the regression coefficients using Eq.(G.4),
ˆ
-1
β = ( X’X ) ( X’Y )

ˆ
So the regression coefficient vector β is
[,1]

[1,] -0.295271027
[2,] 0.001305816
[3,] 0.045605744
[4,] -0.027843496

Furthermore, the regression equation was obtained following

ˆ
Y = -0,2953 + 0,0013 X1 + 0.0456 X2 – 0,0278 X3

Results of computerized using Splus, displays the following output

~~* CHAPTER 5 THE MULTIPLE LINEAR REGRESSION MODEL *~~