- Two students are experimenting with some water in a plastic bottle. The bottle is filled with water and a hole is put in the bottom of the bottle. The students record the time, \(t\) seconds, it takes for the water level to fall to each of 10 given values of the height, \(h \mathrm {~cm}\), above the hole.
Student \(A\) models the data with an equation of the form \(t = a + b \sqrt { h }\)
The data is coded using \(v = t - 40\) and \(w = \sqrt { h }\) and the following information is obtained.
$$\sum v = 626 \quad \sum v ^ { 2 } = 64678 \quad \sum w = 22.47 \quad \mathrm {~S} _ { w w } = 4.52 \quad \mathrm {~S} _ { v w } = - 338.83$$
- Find the equation of the regression line of \(t\) on \(\sqrt { h }\) in the form \(t = a + b \sqrt { h }\)
The time it takes the water level to fall to a height of 9 cm above the hole is 47 seconds.
- Calculate the residual for this data point.
Give your answer to 2 decimal places.
Given that the residual sum of squares (RSS) for the model of \(t\) on \(\sqrt { h }\) is the same as the RSS for the model of \(v\) on \(w\),
- calculate the RSS for these 10 data points.
Student \(B\) models the data with an equation of the form \(t = c + d h\)
The regression line of \(t\) on \(h\) is calculated and the residual sum of squares (RSS) is found to be 980 to 3 significant figures. - With reference to part (c) state, giving a reason, whether Student B's model or Student A's model is the more suitable for these data.