Refer to Exercise 12.25, in which an exploration seismologist wants to develop a regression model for estimating the mean signal-to-noise ratio of seismic waves from earthquakes. The model under consideration is a complete second-order model:

E(y) = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₂ + + β₄x₁² + β₅x₂²

where

 y = Signal-to-noise ratio

x₁ = Frequency of wavelet

x₂ = Amplitude of wavelet

Both the complete model and the reduced model, E(y) = β₀ + β₁x₁ + β₂x₂, were fit to n = 12 data points, with the following results: SSE_C = 159.94, MSE_C = 26.66, SSE_R = 2094.4, MSE_R = 232.7. Compare the two models using a nested model F test at α = .05. What do you conclude?

Data from Exercise 12.25

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