Regression, Correlation and Hypothesis Testing

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Question 64

Medium

A conservationist monitors the population of a rare lizard species on a remote island. The population, $P$ , was recorded every 5 years from 1 January 2000 until 2025. The population size is modelled by the equation

$P = km^n$

where $n$ is the number of years since 1 January 2000 and $k$ and $m$ are constants.

Show that $P = km^n$ can be written as $log_{10} P = \log_{10} k + n \log_{10} m$ .

[2]

The values of $log_{10} P$ against $n$ are plotted on a graph, and a line of best fit is drawn. The line of best fit passes through the points $(0, 1.48)$ and $(25, 2.73)$ . Find estimates for the values of $k$ and $m$ , giving your answers to three significant figures.

[4]

Use your model to predict the year in which the lizard population will first reach 2000.

[2]

Comment on the reliability of your prediction in part (c).

[1]

Regression, Correlation and Hypothesis Testing

Question 64

Regression, Correlation and Hypothesis Testing Questions

Regression, Correlation and Hypothesis Testing

Question 64

Regression, Correlation and Hypothesis Testing Questions