Page 91 - Basic Statistics
P. 91

86




                     Testing criteria:

                            If this test is used at the significance level of , then
                     Accept  H 0 if  F    F(;1;n-2)-table  or     Pr = P ( F > F-actual )     .


                     Reject  H 0  if  F  > F(;1;n-2)-table  or       Pr = P ( F > F-actual ) <  .        ( R12 )



                     5.1.3    THE COEFFICIENT OF DETERMINATION, R               2

                            A  measure  of  how  well  a  linear  regression  model  to  explain  the
                     relationship between independent variables with dependent variables, it can be

                                                                              2
                     seen from the value of koefisien of determination (R ). In partitioning the total
                     sum  of  squares,  an  indication  that  the  model  more  appropriate  if  SS(Reg)

                     greater approaching the total sum of squares. The coefficient of determination

                      2
                     R  is defined as the proportion of SS (Reg) to SS(Total). Thus the coefficient of

                                                                                2
                     determination has a range of values from zero to one. R  value close to 1 means
                     that  the  variation  of  the  variable  Y  increasingly  explained  by  its  the  linear
                     relationship with the independent variables.

                               2
                              R    = SS(Reg) / SS(Total)


                                      ˆ 2
                                                                               2
                                   = β   [  X i  -  (  X i )  / n ]  /  Y j – nY               ( R13 )
                                                          2
                                                                         2
                                                2
                                       1

                     5.1.4   COEFFICIENT TESTING

                          Investigation directly if there are significant changes in the variable Y by

                     changes in variable X, made by testing the coefficient  1. The magnitude of the

                     coefficient  1 is defined as the rate of change in the average value of Y by one

                     unit change in X. To test whether  1 is equal to zero or not, the test hypothesis

                     formulated

                            H 0  :   1 = 0


                            H 1  :   1  0                                                       ( R14 )





                                         ~~* CHAPTER 5   LINEAR REGRESSION MODEL *~~
   86   87   88   89   90   91   92   93   94   95   96