Analysis and Approaches for IBDP Maths Ebook 1 | Page 301

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4. The following table shows the average number of hours per day spent watching television
by the mother and the youngest child of six families.
Hours per day spent
watching television by
a mother ( x )
Hours per day spent
watching television by
her child ( y )
1.8 2.1 2.2 2.4 2.7 3.8
5.5 5.4 4.9 4.9 4.6 4.0
The relationship can be modelled by the regression line with equation y �ax � b .
(a) (i) Find the correlation coefficient r .
(ii) Write down the value of a and of b .
[3]
A social worker believes that the relationship between the average number of hours per
day spent watching television by the mother ( x ) of a family and average number of hours
per day spent watching television by her husband ( w ) can be modelled by a linear
regression equation.
(b)
The social worker describes the correlation as weak and positive. Circle the value
below which best represents the correlation coefficient.
[1]
0.989 0.178 0 � 0.178
� 0.989
(c) The social worker’s model is w�
0.53x. Use her model to predict the average
number of hours per day spent watching television by the father if his wife
watches television for an average of 2.7 hours per day.
[2]
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