The number of breeding pairs of a small parrot species has been declining over recent years.
The table below shows the number of breeding pairs counted, \(pairs\), and the year number, \(year\), for the last 12 years. A scatterplot of this data is also provided.
The association between \(pairs\) and \(year\) is non-linear.
Part A
The scatterplot can be linearised using a logarithmic (base 10) transformation applied to the explanatory variable.
The least squares equation calculated from the transformed data is closest to
- \(\log _{10}(pairs)=2.44-0.0257 \times year\)
- \(\log _{10}(pairs)=151-303 \times year\)
- \(pairs =274-12.3 \times \log _{10}(year)\)
- \(pairs =303-151 \times \log _{10}( year)\)
Part B
A reciprocal transformation applied to the variable \(pairs\) can also be used to linearise the scatterplot.
When a least squares line is fitted to the plot of \(\dfrac{1}{pairs}\) versus \(year\), the largest difference between the actual value and the predicted value occurs at \(year\)
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