Question: The wild rabbits of Australia have recently been seriously threatened by a virus that was accidentally released into their population. (The rabbits themselves were released into Australia decades ago and have become serious pests. The decimation by the virus is not being viewed by many as a bad thing.) Suppose that the table gives the number of rabbits (in millions) remaining at t months after the release of the virus.

1. Use your calculator to fit a regression line to the data. Write the equation of the line. (Keep four decimals.)
2. Do you believe that the linear model found in (a) fits the data well? State the correlation coefficient and explain how it justifies your answer.
3. Use the linear model to estimate the rabbit population 15 months after the release of the virus. Include units. Using the regression equation to predict a value within the boundaries of the given data is called interpolation.
4. Use the linear model to estimate the rabbit population 21 months after the release of the virus. Include units. Using the regression equation to predict a value outside the boundaries of the given data is called extrapolation. This can be unreliable since it is unknown if the trend will continue.
5. What is the physical interpretation of the t-intercept of the graph of the regression line? Your answer should be stated in real-world terms involving rabbits and months, rather than abstract mathematical terms.
6. What is the physical interpretation of the slope of the linear model? Your answer should be stated in real-world terms involving rabbits and months, rather than in abstract mathematical terms.
7. Would you expect this model to be useful to estimate the rabbit population before time t= 0? How about after 22 months? Give reasons, the more specific, the better.

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