4 . The following table shows the lengths x ( in cm ) of the right feet of three students and the corresponding heights y ( in cm ).
Right foot length ( x cm ) 26 24 22 Height ( y cm ) 140 130 135
Two different models are suggested to model the relationship between the variables . The following table shows the estimated heights under two models :
Right foot length ( cm ) x
2
Height ( y cm ) estimated by Model 1 Model 2 y � 2x �90x
� 1200 y �100�
1.02 x 26
26 a 100� 1.02
24 |
b |
24
100� 1.02
|
22 |
188 |
c |
( a ) Write down the values of
( i ) a ;
18
( ii ) b ;
( iii ) c ,
giving the answers correct to the nearest integer .
( b ) Hence , calculate SS res
, the sum of square residuals of the Model 2 .
[ 3 ]
[ 2 ] The model with the smaller sum of square residuals is selected . It is given that the sum of square residuals of the Model 1 is 11837 .
( c ) Determine which model is selected . [ 1 ]
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