The temperature naturally increases as one digs deeper into the continental crust. This phenomenon is called the geothermal gradient. A random sample of continental crust depths (x, in km) was...

The temperature naturally increases as one digs deeper into the continental crust. This phenomenon is called the geothermal gradient. A random sample of continental crust depths (x, in km) was obtained, and the temperature at each depth was recorded ( y, in °C). The data are given in the following table.

c. There is some evidence to suggest that the rate of change in temperature is different according to two depth zones. For example, at small depths, the temperature changes only slightly for each kilometer. However, at large depths, the temperature change is much greater for each kilometer. Use your scatter plot from part (a) to divide the data into two depth zones. Find the estimated regression line and the ANOVA summary table for each zone.

d. Some researchers believe the relationship between depth and temperature is nonlinear and is better modeled by a quadratic curve. Square each depth to create a new list of observations (x2 ). Find the estimated regression line using x2 as the independent variable.

e. Which of these three models do you think is the best? Justify your answer.