Exercise 74
1 . The heights and weights of a group of children are studied . The following table shows the heights x ( in cm ) of five children and the corresponding weights y ( in kg ).
Height ( x cm ) 140 145 150 155 160 Weight ( y kg ) 55 61 58 56 58
It is suggested that the relationship between the variables can be modelled by the regression equation
3 2 y � ax �bx � cx � d , where a , b , c , d � .
( a ) |
( i ) |
Write down the least square regression curve for the weight of children , |
|
|
giving the coefficients correct to 3 significant figures if necessary . |
( ii ) Hence , estimate the weight of a child of height 148 cm .
( b ) ( i ) Write down the coefficient of determination .
( ii ) Hence , interpret the coefficient of determination .
2 . The ages and weights of a group of turtles are studied . The following table shows the ages x ( in years old ) of four turtles and the corresponding weights y ( in g ).
[ 4 ]
[ 2 ]
18
Age ( x years old ) 0.5 1 1.5 2 Weight ( y g ) 20 25 30 23
It is suggested that the relationship between the variables can be modelled by the b regression equation y � ax , where a , b� .
( a ) |
( i ) |
Write down the least square regression curve for the weight of turtles , |
|
|
giving the coefficients correct to 3 significant figures if necessary . |
( ii ) Hence , estimate the weight of a turtle of age 1.25 years old .
( b ) ( i ) Write down the coefficient of determination .
( ii ) Hence , interpret the coefficient of determination .
[ 4 ]
[ 2 ] www . seprodstore . com
273