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Question id: 53. This question is similar to one that appeared in an IB Standard paper in 2014. The use of a calculator is allowed.

### Correlation

The following table shows the average weights for given heights in a population of men.

 Heights (x cm) 160 165 170 175 180 185 Weights ( y kg) 65.1 67.9 70.1 72.8 75.4 77.2

(a) The relationship between the variables is modelled by the regression equation $$y =­ ax + b$$. Write down the value of $$a$$ and of $$b$$.

(b) Use this relationship to estimate the weight of a man whose height is 177 cm.

(c) Find the correlation coefficient.

(d) State which two of the following describe the correlation between the variables.

• strong
• zero
• positive
• negative
• no correlation
• weak
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