The scatterplot below plots the average monthly ice cream consumption, in litres/person, against average monthly temperature, in °C. The data for the graph was recorded in the Northern Hemisphere.
When a least squares line is fitted to the scatterplot, the equation is found to be:
consumption = 0.1404 + 0.0024 × temperature
The coefficient of determination is 0.7212
- Draw the least squares line on the scatterplot graph above. (1 mark)
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- Determine the value of the correlation coefficient \(r\).
- Round your answer to three decimal places. (1 mark)
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- Describe the association between average monthly ice cream consumption and average monthly temperature in terms of strength, direction and form. (1 mark)
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\begin{array} {|l|c|}
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\rule{0pt}{2.5ex} \textbf{strength} \rule[-1ex]{0pt}{0pt} & \quad \quad \quad \quad \quad \quad \quad \quad \\
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\rule{0pt}{2.5ex} \textbf{direction} \rule[-1ex]{0pt}{0pt} & \\
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\rule{0pt}{2.5ex} \textbf{form} \rule[-1ex]{0pt}{0pt} & \\
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\end{array} - Referring to the equation of the least squares line, interpret the value of the intercept in terms of the variables consumption and temperature. (1 mark)
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- Use the equation of the least squares line to predict the average monthly ice cream consumption, in litres per person, when the monthly average temperature is –6°C. (1 mark)
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- Write down whether this prediction is an interpolation or an extrapolation. (1 mark)
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