Your Practice Set – Applications and Interpretation for IBDP Mathematics
74
Paper 1 – Non-Linear Regressions
Example
The noon temperatures of some towns are studied . The following table shows the altitude
x ( in m ) of five towns and the corresponding noon temperature y ( in o C ).
Altitude ( x m ) 50 100 150 200 250 Noon temperature o
( y C ) 24 26 32 33 32
It is suggested that the relationship between the variables can be modelled by the regression equation
2 y � ax �bx � c , where a , b , c� .
( a ) |
( i ) |
Write down the least square regression curve for the noon temperature , |
|
|
giving the coefficients correct to 3 significant figures if necessary . |
( ii ) Hence , estimate the noon temperature of a town of altitude 125 m .
( b ) ( i ) Write down the coefficient of determination .
( ii ) Hence , interpret the coefficient of determination .
[ 4 ]
[ 2 ]
Solution
( a ) ( i ) y � � x � x � A2
2
0.000371 0.153 17
( b ) ( i )
( ii ) The estimated noon temperature ��0.0003714285714 ( 125 ) �0.1534285714 ( 125 ) �17 o
� 30.375 C o
� 30.4 C A1
2
R � 0.9889336016
2
R � 0.989 A1
2
( A1 ) for substitution
[ 4 ]
( ii ) 98.9 % of the variability of the data is explained by the regression model .
A1 [ 2 ]
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