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Date May 2014 Marks available 1 Reference code 14M.2.sl.TZ1.3
Level SL only Paper 2 Time zone TZ1
Command term Write down Question number 3 Adapted from N/A

Question

The following table shows the average weights ( y kg) for given heights (x cm) in a population of men.

 

Heights (x cm) 165 170 175 180 185
Weights (y kg) 67.8 70.0 72.7 75.5 77.2

The relationship between the variables is modelled by the regression equation \(y = ax + b\).

Write down the value of \(a\) and of \(b\).

[2]
a(i).

The relationship between the variables is modelled by the regression equation \(y = ax + b\).

Hence, estimate the weight of a man whose height is 172 cm.

[2]
a(ii).

Write down the correlation coefficient.

[1]
b(i).

State which two of the following describe the correlation between the variables.

strong      zero      positive
negative      no correlation      weak
[2]
b(ii).

Markscheme

\(a = 0.486\)   (exact)     A1     N1

\(b =  - 12.41\)   (exact), \(-12.4\)     A1     N1

[2 marks]

a(i).

correct substitution     (A1)

eg     \(0.486(172) - 12.41\)

\(71.182\)

\(71.2\) (kg)     A1     N2

[2 marks]

a(ii).

\(r = 0.997276\)

\(r = 0.997\)     A1     N1

[1 mark]

b(i).

strong, positive (must have both correct)     A2     N2

[2 marks]

b(ii).

Examiners report

[N/A]
a(i).
[N/A]
a(ii).
[N/A]
b(i).
[N/A]
b(ii).

Syllabus sections

Topic 5 - Statistics and probability » 5.4 » Linear correlation of bivariate data.
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