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A farmer collected data on the annual rainfall, x cm, and the annual yield of peas, p tonnes per acre - Edexcel - A-Level Maths Statistics - Question 4 - 2011 - Paper 1

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A farmer collected data on the annual rainfall, x cm, and the annual yield of peas, p tonnes per acre. The data for annual rainfall was coded using v = \frac{x-5}{1... show full transcript

Worked Solution & Example Answer:A farmer collected data on the annual rainfall, x cm, and the annual yield of peas, p tonnes per acre - Edexcel - A-Level Maths Statistics - Question 4 - 2011 - Paper 1

Step 1

Find the equation of the regression line of p on v in the form p = a + bv

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Answer

To find the regression line, we use the formula:

  1. The gradient (b) is given by: b=SpmSw=1.6885.753≈0.293b = \frac{S_{pm}}{S_w} = \frac{1.688}{5.753} \approx 0.293

  2. The intercept (a) can be calculated as: a=pˉ−b⋅vˉ=1.168−0.293⋅4.42≈1.168−1.293=−0.125a = \bar{p} - b \cdot \bar{v} = 1.168 - 0.293 \cdot 4.42 \approx 1.168 - 1.293 = -0.125

  3. Thus, the equation of the regression line is: p=−0.125+0.293vp = -0.125 + 0.293v

Step 2

Using your regression line estimate the annual yield of peas per acre when the annual rainfall is 85 cm

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Answer

First, we need to calculate the value of v when x = 85 cm: v=85−510=8010=8v = \frac{85 - 5}{10} = \frac{80}{10} = 8

Using the regression equation:
p=−0.125+0.293⋅8≈−0.125+2.344=2.219p = -0.125 + 0.293 \cdot 8 \approx -0.125 + 2.344 = 2.219

Therefore, the estimated annual yield of peas per acre is approximately 2.219 tonnes.

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