Your Practice Set – Applications and Interpretation for IBDP Mathematics
3 . The lengths and weights of a group of salmons are studied . The following table shows the lengths x ( in cm ) of three salmons and the corresponding weights y ( in g ).
Length ( x cm ) 70 80 90 Weight ( y g ) 6700 7400 7500
Two different models are suggested to model the relationship between the variables . The following table shows the estimated weights under two models :
Weight ( y g ) estimated by Model 1 Model 2
Length ( x cm ) y�40x� 4000 y �4600 � 1.01 x 70 6800 a
80 |
b |
80 4600
� 1.01
|
90 |
7600 |
c |
( a ) Write down the values of
( i ) a ;
( 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 1 .
[ 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 2 is 28400000 .
( c ) Determine which model is selected . [ 1 ]
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