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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
Question 4
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
Answer
To find the regression line of ( p ) on ( v ), we use the formula: [ p = \bar{p} + b(\bar{v} - v) ] Where:
- ( b = \frac{S_{pv}}{S_w} )
- ( S_{pv} = 1.688 ), ( S_w = 5.753 ) Calculating ( b ): [ b = \frac{1.688}{5.753} \approx 0.293 ] Now, substituting ( \bar{p} ) and ( \bar{v} ): [ p = 3.22 + 0.293(v - 4.42) ] Thus, the regression line is: [ p = 1.92 + 0.293v ]
Step 2
Using your regression line estimate the annual yield of peas per acre when the annual rainfall is 85 cm
Answer
First, we need to convert the annual rainfall into the standardized variable ( v ). [ v = \frac{85 - 5}{10} = 8 ] Now, substituting ( v = 8 ) into the regression equation: [ p = 1.92 + 0.293(8) ] [ p = 1.92 + 2.344 = 4.264 ] Therefore, the estimated annual yield of peas per acre when the annual rainfall is 85 cm is approximately ( 4.3 ) tonnes.