Distinguish between interpolation and extrapolation.

A biologist has collected data on the wingspan (in cm) of a bird species against its age (in years). A least-squares regression line has been fitted to data points from birds aged 2 to 8 years old. The biologist uses this line to predict the wingspan of a 5-year-old bird from this species. Which classification best describes this prediction?

A marine biologist collects data on the average water temperature (°C) versus depth (metres) at a coastal reef site. The data are shown in the table below. A least-squares regression line is fitted to the data and has the equation \(T = 26.2 - 0.35d\), where \(T\) is the temperature in °C and \(d\) is the depth in metres. (a) Use the regression equation to predict the water temperature at a depth of \(35\) metres. Classify this prediction as interpolation or extrapolation and justify your classification. (2 marks) (b) Use the regression equation to predict the water temperature at a depth of \(90\) metres. Classify this prediction as interpolation or extrapolation and justify your classification. (2 marks)

A biologist fitted a least-squares regression line to data showing the relationship between the temperature (in $^{\circ}\mathrm{C}$) and the respiration rate (in $\mu\mathrm{mol\ s^{-1}}$) of plant seedlings. The data was collected for temperatures between $15^{\circ}\mathrm{C}$ and $35^{\circ}\mathrm{C}$. The fitted equation is $\hat{r} = 0.82t + 1.5$, where $\hat{r}$ is the predicted respiration rate and $t$ is temperature. (a) Use the regression equation to predict the respiration rate when the temperature is $28^{\circ}\mathrm{C}$. (1 mark) (b) State whether your prediction in part (a) is an example of interpolation or extrapolation, and justify your answer. (1 mark) (c) Explain why it would be inappropriate to use this equation to predict the respiration rate at $50^{\circ}\mathrm{C}$. (1 mark)