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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}... 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 of p on v, we need the values of the regression coefficients a and b.

  1. Calculate the slope, b: b=SpSpm=1.6881.168≈1.44b = \frac{S_p}{S_{pm}} = \frac{1.688}{1.168} \approx 1.44

  2. Calculate the intercept, a:

    a=p‾−b⋅v‾=3.22−1.44⋅4.42≈3.22−6.37≈−3.15a = \overline{p} - b \cdot \overline{v} = 3.22 - 1.44 \cdot 4.42 \approx 3.22 - 6.37 \approx -3.15

  3. The equation of the regression line is:

    p=−3.15+1.44vp = -3.15 + 1.44 v

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 code the value of x = 85 cm into v:

v=85−510=8010=8v = \frac{85 - 5}{10} = \frac{80}{10} = 8

Now we substitute v into the regression equation:

p=−3.15+1.44⋅8\n=−3.15+11.52\n=8.37p = -3.15 + 1.44 \cdot 8\n = -3.15 + 11.52 \n = 8.37

Therefore, the estimated annual yield of peas per acre when the annual rainfall is 85 cm is approximately 8.37 tonnes.

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