The table below shows the height, in metres, and the age, in years, for 11 plantation trees. A scatterplot displaying this data is also shown.
Question 11
A reciprocal transformation applied to the variable age can be used to linearise the scatterplot.
With \(\dfrac{1}{\textit{age}}\) as the explanatory variable, the equation of the least squares line fitted to the linearised data is closest to
- \(\textit{height}\ =-13.04 + 40.22 \times \dfrac{1}{\textit{age}}\)
- \(\textit{height}\ =-10.74+8.30 \times \dfrac{1}{\textit{age}}\)
- \(\textit{height}\ =2.14 + 0.63 \times \dfrac{1}{\textit{age}}\)
- \(\textit{height}\ =13.04-40.22 \times \dfrac{1}{\textit{age}}\)
- \(\textit{height}\ =16.56-22.47 \times \dfrac{1}{\textit{age}}\)
Question 12
The scatterplot can also be linearised using a logarithm (base 10) transformation applied to the variable age.
The equation of the least squares line is
\(\textit{height }=-3.8+12.6 \times \log _{10}(\textit{age}) \)
Using this equation, the age, in years, of a tree with a height of 8.52 m is closest to
- 7.9
- 8.9
- 9.1
- 9.5
- 9.9