The article “Permanent Deformation Characterization of

Chapter 8, Problem 14E

(choose chapter or problem)

The article “Permanent Deformation Characterization of Subgrade Soils from RLT Test” (A. Puppala, L. Mohammad, et al., Journal of Materials in Civil Engineering, 1999:274–282) presents measurements of plastic strains (in percent) on soils at various confining and deviatoric stresses in kPa. The following table presents the plastic strains \((y)\), the confining stress \((x_1)\), and the deviatoric stress \((x_2)\) for tests on a sandy soil.

a. Fit the model \(y=\beta_0+\beta_1x_1+\beta_2x_2+\varepsilon\). Plot the residuals versus the fitted values. Does the model seem appropriate?

b. Fit the model ln \(y=\beta_0+\beta_1 \ln x_1+\beta_2 \ln x_2+\varepsilon\). Plot the residuals versus the fitted values. Does the model seem appropriate?

c. Use the more appropriate of the models from (a) and (b) to predict y when \(x_1=50\) and \(x_2=100\).

d. Is the model you used in part (c) improved by including an interaction term? Explain.

Equation Transcription:

Text Transcription:

(y)

(x_1)

(x_2)

x_1

x_2

x_1

x_2

y=beta_0+beta_1x_1+beta_2x_2+varepsilon

y=beta_0+beta_1 ln x_1+beta_2 ln x_2+varepsilon

x_1=50

x_2=100