AQA S1 2011 June — Question 3

Exam BoardAQA
ModuleS1 (Statistics 1)
Year2011
SessionJune
TopicLinear regression
TypeCalculate y on x from raw data table
3
  1. During a particular summer holiday, Rick worked in a fish and chip shop at a seaside resort. He suspected that the shop's takings, \(\pounds y\), on a weekday were dependent upon the forecast of that day's maximum temperature, \(x ^ { \circ } \mathrm { C }\), in the resort, made at 6.00 pm on the previous day. To investigate this suspicion, he recorded values of \(x\) and \(y\) for a random sample of 7 weekdays during July.
    \(\boldsymbol { x }\)23182719252022
    \(\boldsymbol { y }\)4290318851063829505742644485
    1. Calculate the equation of the least squares regression line of \(y\) on \(x\).
    2. Estimate the shop's takings on a weekday during July when the maximum temperature was forecast to be \(24 ^ { \circ } \mathrm { C }\).
    3. Explain why your equation may not be suitable for estimating the shop's takings on a weekday during February.
    4. Describe, in the context of this question, a variable other than the maximum temperature, \(x\), that may affect \(y\).
  2. Seren, who also worked in the fish and chip shop, investigated the possible linear relationship between the shop's takings, \(\pounds z\), recorded in \(\pounds 000\) s, and each of two other explanatory variables, \(v\) and \(w\).
    1. She calculated correctly that the regression line of \(z\) on \(v\) had a \(z\)-intercept of - 1 and a gradient of 0.15 . Draw this line, for values of \(v\) from 0 to 40, on Figure 1 on page 4.
    2. She also calculated correctly that the regression line of \(z\) on \(w\) had a \(z\)-intercept of 5 and a gradient of - 0.40 . Draw this line, for values of \(w\) from 0 to 10, on Figure 2 below. \begin{figure}[h]
      \captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{767ec629-6350-41d9-bbb9-e059a5fd8c70-4_792_604_680_717}
      \end{figure} \begin{figure}[h]
      \captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{767ec629-6350-41d9-bbb9-e059a5fd8c70-4_792_696_1692_687}
      \end{figure}
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