#591 Using the equations developed in class, solve for the

Using the equations developed in class, solve for the - Math

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1. Data from a permeability test on sand gave the following gradient-flow rate results (this is a test that you will conduct in the Geotechnical laboratory course in spring of Junior year):

gradient i 0.0 0.22 0.41 0.59 0.80 1.01 1.09

flow q (mm/s) 0.0 0.38 0.81 1.15 1.54 1.91 2.25

1. (a) Using the equations developed in class, solve for the "best fit" straight line through the data using least-squares regression, by hand, presuming i is the independent variable (ie use the equations based on the sums Σx, Σy, Σxy, Σx2, N).
2. (b) Solve for the best fit straight line again using the statistical form of the solution, with slope = sxy/sxx and y-intercept = (Mean y) - slope* (mean x). Compare with (a).
3. (c) It is known from Darcy's law in soil mechanics that the flow rate is directly proportional to the gradient and MUST be zero when the gradient is zero, ie q = k×i where k is a constant. How can we determine the best fit slope k and ensure that the line goes through the origin (0,0)?
4. (d) Compute an unbiased estimate of the variance of the error, 𝑠2= 𝑛𝑛−2 (1−𝑆𝑥𝑦2𝑆𝑥𝑥𝑆𝑦𝑦)𝑠𝑦𝑦
5. (e) Using a spreadsheet program, plot the data along with

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