The article “Influence of Freezing Temperature on Hydraulic
Conductivity of Silty Clay†describes a study of factors affecting
hydraulic conductivity of soils. The measurements of hydraulic
conductivity (HC) in units of 10-8 cm/s, initial void ratio (IVR)
and thawed void ratio (TVR) for 12 specimens of silty clay are
presented in Project.MTW. HC:1.010,
1.120,1.040,1.300,1.010,1.040,0.955,1.150,1.230,1.280,1.230,1.300.
IVR:0.84,0.88,0.85 0.95,0.88,0.86,0.85,0.89,0.90,0.94,0.88,0.90.
TVR: 0.81,0.85,0.87,0.92,0.84,0.85,0.85,0.86,0.85,0.92,0.88,0.92.
a) [4 pts]Draw a scatterplot for the relationship between HC and
IVR, and explain it. b) [5 pts]Calculate the coefficient of
correlation between HC and TVR, and explain the relationship. c) [4
pts]Fit a linear regression model to predict HC using IVR and TVR.
d) [3 pts]Interpret the coefficients of the fitted model in part ©.
e) [4 pts]At 5% significant level test which of the two predictors
has/have significant linear relationship with HC. f) [4 pts]At 5%
significant level test the usefulness/goodness of the model. g) [2
pts]Calculate the coefficient of determination and interpret its
meaning. h) [2 pts]What is the estimate of the error variance for
this model? i) [2 pts]Predict HC of a silty clay with the IVR of
0.885 and TVR of 0.91. j) [2 pts]At 5% significant level predict HC
of a silty clay with IVR of 0.885 and TVR of 0.91. k) [2 pts]At 5%
significant level predict the mean HC of a silty clays with IVR of
0.885 and TVR of 0.91. l) [6 pts]Check the assumptions of the
fitted model.
