An exploration seismologist wants to develop a model that will allow him to estimate the average signal-to-noise ratio of an earthquake’s seismic wave, y, as a function of two independent variables: 

x₁ = Frequency (cycles per second)

x₂ = Amplitude of the wavelet

a. Identify the independent variables as quantitative or qualitative.

b. Write the first-order model for E(y).

c. Write a model for E(y) that contains all first-order and interaction terms. Sketch typical response curves showing E(y), the mean signal-to-noise ratio, versus x₂, the amplitude of the wavelet, for different values of x₁ (assume that x₁ and x₂ interact).

d. Write the complete second-order model for E(y).