AQA S1 2007 June — Question 5

Exam BoardAQA
ModuleS1 (Statistics 1)
Year2007
SessionJune
TopicLinear regression
TypeCalculate y on x from raw data table

5 Bob, a gardener, measures the time taken, \(y\) minutes, for 60 grams of weedkiller pellets to dissolve in 10 litres of water at different set temperatures, \(x ^ { \circ } \mathrm { C }\). His results are shown in the table.
\(\boldsymbol { x }\)1620242832364044485256
\(\boldsymbol { y }\)4.74.33.83.53.02.72.42.01.81.61.1
  1. State why the explanatory variable is temperature.
  2. Calculate the equation of the least squares regression line \(y = a + b x\).
    1. Interpret, in the context of this question, your value for \(b\).
    2. Explain why no sensible practical interpretation can be given for your value of \(a\).
    1. Estimate the time taken to dissolve 60 grams of weedkiller pellets in 10 litres of water at \(30 ^ { \circ } \mathrm { C }\).
    2. Show why the equation cannot be used to make a valid estimate of the time taken to dissolve 60 grams of weedkiller pellets in 10 litres of water at \(75 ^ { \circ } \mathrm { C }\). (2 marks)