Analysis and Approaches for IBDP Maths Ebook 1 | Page 298

Your Practice Set – Analysis and Approaches for IBDP Mathematics
97
Paper 2 Section A – Describe the correlations
Example
The following table shows the average weights ( y kg) for given heights ( x cm) in a
group of people.
Heights ( x cm) 156 160 164 168 172 176
Weights ( y kg) 52 58 59 65 67 72
(a)
The relationship between the variables is modelled by the regression equation
y �ax � b .
(i) Write down the value of a and of b .
(ii)
Hence, estimate the weight of a person whose height is 170 cm.
(b) (i) Write down the correlation coefficient.
[4]
(ii)
State which two of the following describe the correlation between the
variables.
positive strong zero
negative weak no correlation
[3]
Solution
(a) (i) a � 0.95
A1 N1
b �� 95.53333333
b �� 95.5
A1 N1
(ii) Correct Substitution
The estimated weight
�0.95(170) � 95.53333333
(A1) for substitution
� 65.96666667
� 66.0 kg A1 N2
(b) (i) r � 0.9880809318
r � 0.988
A1 N1
(ii) Strong, Positive A2 N2
[4]
[3]
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