- A random sample of 10 cars of different makes and sizes is taken and the published miles per gallon, \(p\), and the actual miles per gallon, \(m\), are recorded. The data are coded using variables \(x = \frac { p } { 10 }\) and \(y = m - 25\)
The results for the coded data are summarised below.
| \(\boldsymbol { x }\) | 6.89 | 3.67 | 5.92 | 5.04 | 4.87 | 3.92 | 4.71 | 5.14 | 3.65 | 5.23 |
| \(\boldsymbol { y }\) | 30 | 3 | 22 | 15 | 13 | 8 | 15 | 13.5 | 3 | 19 |
(You may use \(\sum y ^ { 2 } = 2628.25 \quad \sum x y = 768.58 \quad \mathrm {~S} _ { x x } = 9.25924 \quad \mathrm {~S} _ { x y } = 74.664\) )
- Show that \(\mathrm { S } _ { y y } = 626.025\)
- Find the product moment correlation coefficient between \(x\) and \(y\).
- Give a reason to support fitting a regression model of the form \(y = a + b x\) to these data.
- Find the equation of the regression line of \(y\) on \(x\), giving your answer in the form \(y = a + b x\).
Give the value of \(a\) and the value of \(b\) to 3 significant figures.
A car's published miles per gallon is 44 - Estimate the actual miles per gallon for this particular car.
- Comment on the reliability of your estimate in part (e). Give a reason for your answer.