Coir fiber, derived from coconut, is an eco-friendly material with great potential for reducing the seepage of water when mixed with soil; this is an important application in new building construction. The table screenshot contains data from 49 measurements of water seepage velocity from different soil along with the concentration of fiber in the soil (%), average length of the fiber, and the hydraulic gradient of the fiber.

1. Create scatterplots of all combination of the four variables and calculate their correlation coefficients and comment on what the result indicates with respect to any model you might fit to seepage velocity from the other three variables.
2. Fit a multiple regression model in R with seepage velocity as the response and the other three variables as predictors. Report the results of the model and comment following the process outlined in class.
3. Fit a second multiple regression model using just length and gradient as predictors. Report the results and comment. Comment on any differences from the result in part (2) and explain the differences.
4. Fit a third model using the three predictor variables from part (2), but this time fit a "complete second order model" (include quadratic terms for the predictors as well as all combinations of second order interactions). Report the results and comment.
5. Fit a fourth model using the approach in part (4), except this time center the predictor variables in the quadratic and interaction terms. Report the results and comment. Comment on any differences from the result in part (4) and explain the differences.
6. Fit a fifth model that is identical to the model in part (5), except remove any predictors that are not significant. Report the results and comment. Comment on any differences from the result in part (5) and explain the differences.
7. Which model of the five would you recommend we use? Explain.

cont Ingth grad vel 0.0 0.400 0.027 2 0.0 0.716 0.050 3 0.0 0.925 0.080 4 0.0 O 1.098 0.099 5 0.0 1.226 0.107 6 0.0 1.427 0.140 7 0.0 1.709 0.178 0.0 1.872 0.200 9 0.5 50 0.380 0.022 10 0.5 50 0.774 0.040 11 0.5 50 1.056 0.060 12 0.5 50 1.329 0.111 13 0.5 50 1.598 0.158 14 0.5 50 1.799 0.188 15 1.0 50 0.410 0.026 16 1.0 50 0.577 0.038 17 1.0 50 0.748 0.049 18 1.0 50 0.927 0.060 19 1.0 50 1.090 0.070 20 1.0 50 1.239 0.088 21 1.0 50 1.496 0.111 22 1.0 50 1.744 0.134 23 1.0 50 1.915 0.145 24 1.5 50 0.444 0.01425 1.5 50 0.821 0.037 26 1.5 50 1.141 0.058 27 1.5 50 1.474 0.082 28 1.5 50 1.581 0.112 29 1.5 50 1.983 0.144 30 1.0 25 0.462 0.028 31 1.0 25 0.705 0.059 32 1.0 25 0.987 0.084 33 1.0 25 1.154 0.101 34 1.0 25 1.479 0.150 35 1.0 25 1.786 0.194 36 1.0 25 1.957 0.218 37 1.0 40 0.419 0.030 38 1.0 40 0.705 0.050 39 1.0 40 0.979 0.068 40 1.0 40 1.226 0.091 41 1.0 40 1.470 0.126 42 1.0 40 1.744 0.168 43 1.0 60 0.436 0.034 44 1.0 0.650 0.051 45 1.0 60 0.889 0.068 46 1.0 60 1.222 0.093 47 1.0 60 1.477 0.112 48 1.0 60 1.726 0.139 49 1.0 60 1.983 0.173