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Date	May Specimen paper	Marks available	7	Reference code	SPM.1.AHL.TZ0.12
Level	Additional Higher Level	Paper	Paper 1	Time zone	Time zone 0
Command term	Determine	Question number	12	Adapted from	N/A

Question

Product research leads a company to believe that the revenue ( $R$ ) made by selling its goods at a price ( $p$ ) can be modelled by the equation.

$R\left( p \right) = cp{{\text{e}}^{dp}}$ , $c$ , $d \in \mathbb{R}$

There are two competing models, A and B with different values for the parameters $c$ and $d$ .

Model A has $c$ = 3, $d$ = −0.5 and model B has $c$ = 2.5, $d$ = −0.6.

The company experiments by selling the goods at three different prices in three similar areas and the results are shown in the following table.

The company will choose the model with the smallest value for the sum of square residuals.

Determine which model the company chose.

Markscheme

(Model A)

$R = 3p{{\text{e}}^{ - 0.5p}}$ M1

predicted values

(A1)

$S{S_{res}} = {\left( {1.8196 - 1.5} \right)^2} + {\left( {2.2073 - 1.8} \right)^2} + {\left( {2.0082 - 1.5} \right)^2}$ (M1)

= 0.5263… A1

(Model B)

$R = 2.5p{{\text{e}}^{ - 0.6p}}$

predicted values

(A1)

$S{S_{res}} =$ 0.170576… A1

chose model B A1

Note: Method marks can be awarded if seen for either model A or model B. Award final A1 if it is a correct deduction from their calculated values for A and B.

[7 marks]

Examiners report

[N/A]

Syllabus sections

Topic 4—Statistics and probability » AHL 4.13—Non-linear regression

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EXM.3.AHL.TZ0.9f.ii:
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EXM.3.AHL.TZ0.7a.ii:
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22M.3.AHL.TZ1.1b.iv:
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21M.2.AHL.TZ1.4b.ii:
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EXM.3.AHL.TZ0.9f.iii:
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