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The number of daylight hours H at noon in City X was measured on the 21st of each month for eight consecutive months (m=1 for January, …, m=8 for August). The results are shown below; the value for May (m=5) was lost in transcription.
Assuming the data follows a linear model over this period, find the regression line of H on m for the seven known points.
Use your line to estimate the daylight hours on the 21st of May (m=5).
Explain why your line should not be used to estimate the month m at which H=17.0h.
Explain in context why your line should not be used to predict the daylight hours on the 21st of December (m=12).
State a more appropriate model for H over an entire year. You are not expected to calculate any parameters.
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Lucy operates a smoothie stall and has observed that warmer temperatures lead to higher sales of her smoothies. Over six days she recorded the maximum daily temperature, T(°C), and the number of smoothies sold, S. The results are:
The relationship between S and T is modeled by the regression line S=aT+b.
Find the values of a and b.
Write down the correlation coefficient r.
Using your regression equation, estimate the number of smoothies sold when T=21°C.
Interpret the value of the slope a in the context of the problem.
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