A 3 ft deep fish pond in the shape of a hemisphere has a volume of 56.549 ft3 when it is full. These data have been collected relating depth to volume in the pond:

a. Find the equation of the least squares line that estimates the volume as a function of depth.
b. Plot your equation from 8a with the data points, and decide whether you think it is a good fit.
c. Calculate the values of r and r2 for a linear model. What do they tell you about whether or not the least squares line is a good fit?
d. Find quadratic and cubic models to estimate the volume for different depths. Graph these curves with the data.
e. Which of the three regression models (linear, quadratic, or cubic) appears to fit the data best?
f. What are the values of R2 for the quadratic and cubic models? How does this confirm or refute your answer to 8e?

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0.5 1.0 1.5 2.0 2.5 3.0 Depth (ft) Volume (ft3 0 2.225 8.378 17.67129.322 42.542 56.549