4 [Figure 1, printed on the insert, is provided for use in this question.]
Roseen is a self-employed decorator who wishes to estimate the times that it will take her to decorate bedrooms based upon their floor areas. She records the floor area, \(x \mathrm {~m} ^ { 2 }\), and the decorating time, \(y\) hours, for each of 10 bedrooms she has recently decorated.
| \(\boldsymbol { x }\) | 11.0 | 22.0 | 7.5 | 21.0 | 13.0 | 16.5 | 14.0 | 16.0 | 18.5 | 20.5 |
| \(\boldsymbol { y }\) | 15.0 | 35.0 | 16.0 | 23.5 | 24.0 | 17.5 | 14.5 | 27.5 | 22.5 | 34.5 |
- On Figure 1, plot a scatter diagram of these data.
- Calculate the equation of the least squares regression line of \(y\) on \(x\).
- Draw your regression line on Figure 1.
- Use your regression equation to estimate the time that Roseen will take to decorate a bedroom with a floor area of \(15 \mathrm {~m} ^ { 2 }\).
- Making reference to Figure 1, comment on the likely reliability of your estimate in part (d)(i).