<p>An energy company is studying the relationship between the average daily temperature, \(x\) (in degrees Celsius), and the amount of electricity consumed, \(y\) (in megawatt-hours MWh). For a random sample of ten days, the records are shown in the table below.</p>
<div class="content-block content-block--table"><div class="table-container"><table><thead><tr><th style="text-align: left; --cell-justify: flex-start">Average daily temperature (\(x{}^\circ\)C)</th><th style="text-align: left; --cell-justify: flex-start">\(20\)</th><th style="text-align: left; --cell-justify: flex-start">\(22\)</th><th style="text-align: left; --cell-justify: flex-start">\(24\)</th><th style="text-align: left; --cell-justify: flex-start">\(26\)</th><th style="text-align: left; --cell-justify: flex-start">\(28\)</th><th style="text-align: left; --cell-justify: flex-start">\(30\)</th><th style="text-align: left; --cell-justify: flex-start">\(32\)</th><th style="text-align: left; --cell-justify: flex-start">\(34\)</th><th style="text-align: left; --cell-justify: flex-start">\(36\)</th><th style="text-align: left; --cell-justify: flex-start">\(38\)</th></tr></thead><tbody><tr><td style="text-align: left; --cell-justify: flex-start">Electricity consumption (\(y\) MWh)</td><td style="text-align: left; --cell-justify: flex-start">\(12.5\)</td><td style="text-align: left; --cell-justify: flex-start">\(12.8\)</td><td style="text-align: left; --cell-justify: flex-start">\(13.2\)</td><td style="text-align: left; --cell-justify: flex-start">\(14.0\)</td><td style="text-align: left; --cell-justify: flex-start">\(14.7\)</td><td style="text-align: left; --cell-justify: flex-start">\(16.2\)</td><td style="text-align: left; --cell-justify: flex-start">\(16.2\)</td><td style="text-align: left; --cell-justify: flex-start">\(19.9\)</td><td style="text-align: left; --cell-justify: flex-start">\(22.3\)</td><td style="text-align: left; --cell-justify: flex-start">\(29.5\)</td></tr></tbody></table></div></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Draw a scatter diagram for these values, labelling the axes clearly.</span><span class="inline-marks">[1]</span></div></li></ol>
<p>It is thought that the electricity consumption and average daily temperature can be modelled by one of the formulae\[y = a + bx^2, \quad y = c + dx,\]where&nbsp;\(a\), \(b\), \(c\) and \(d\) are constants.</p>
<ol class="abc-list" start="2"><li><div class="list-item-content"><span class="list-item-text">Find the value of the product moment correlation coefficient between</span><span class="inline-marks">[2]</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">\(x\) and \(y\),</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(x^2\) and \(y\).</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Using your answers in parts (a) and (b), explain which of \(y = a + bx^2\) and \(y = c + dx\) is the better model and find the equation of a suitable regression line for this model.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Use the equation of your regression line to estimate the electricity consumption on a day with an average temperature of \(37{}^\circ\)C. Comment on the reliability of your estimate.</span><span class="inline-marks">[2]</span></div></li></ol>
<p>In some regions, temperature is measured in degrees Fahrenheit instead of degrees Celsius. A temperature of \(C\) degrees Celsius is equivalent to \(F\) degrees Fahrenheit, where&nbsp;\(F = \frac{9}{5}C + 32\).</p>
<ol class="abc-list" start="5"><li><div class="list-item-content"><span class="list-item-text">Rewrite the equation of your regression line found in part (c) in terms of \(y\) and \(F\), where&nbsp;\(F\) is the average daily temperature in degrees Fahrenheit.</span><span class="inline-marks">[1]</span></div></li></ol>

An energy company is studying the relationship between the average daily temperature, \(x\) (in degrees Celsius), and the amount of electricity consumed, \(y\) (in megawatt-hours MWh). For a random sample of ten days, the records are shown in the table below.

Draw a scatter diagram for these values, labelling the axes clearly.

It is thought that the electricity consumption and average daily temperature can be modelled by one of the formulae\[y = a + bx^2, \quad y = c + dx,\]where \(a\), \(b\), \(c\) and \(d\) are constants.

Find the value of the product moment correlation coefficient between

Using your answers in parts (a) and (b), explain which of \(y = a + bx^2\) and \(y = c + dx\) is the better model and find the equation of a suitable regression line for this model.

Use the equation of your regression line to estimate the electricity consumption on a day with an average temperature of \(37{}^\circ\)C. Comment on the reliability of your estimate.

In some regions, temperature is measured in degrees Fahrenheit instead of degrees Celsius. A temperature of \(C\) degrees Celsius is equivalent to \(F\) degrees Fahrenheit, where \(F = \frac{9}{5}C + 32\).

Rewrite the equation of your regression line found in part (c) in terms of \(y\) and \(F\), where \(F\) is the average daily temperature in degrees Fahrenheit.

2025 VJC P2 Q11

2025 VJC P2 Q11