Impact of Educational Institutions on Literacy Rate...

Thus the normal equation of multiple regression analysis are:

666.6 = 10 a + 1169 b ₁ + 302 b ₂

(1)

76384.8 = 1169 a + 175981 b ₁ + 43198 b ₂

(2)

19684.3 = 302 a + 43198 b ₁ + 10980 b ₂

(3)

This set of matrix equations can also be written in matrix form:

 666.6 

 10

1169

302   a 







  

 76384.8  =  1169 175981 43198   1 

 b

 19684.3 



 302



43198

10980   b 2  

Or, C = AX

 10

1169

302 

 666.6 









Where, A =  1169 175981 43198  ,

C =  76384.8 

 302 43198 10980 



 19684.3 



 a 

 

And unknown vector, X =  b 1  Therefore, X = A -1 C

 b 

 2 

The above equation can be solved manually by matrix algebra and find out the

value of unknown vector X . Hence, a = 74.6135, b ₁ = 0.0613 and b ₂ = –0.5010.

Therefore, in this case the regression equation according to matrix method can

be expressed as:

Y _c = 74.6135 + 0.0613 b ₁ – 0.5010 b 2

It is clear estimate that the estimated value of literacy rate increases by 0.0613%

for each additional unit in primary school and it decreases by 0.5010% for each unit

change of upper primary school.

Multiple Correlation Coefficient:

  Y  Yc  2

R 2

YX 1 X 2

=

  Y  Y   2

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