Many parts of the USA are experiencing increased erosion along waterways due to increased flow from global climate change. The report “Evaluation and Assessment of Environmentally Sensitive Stream Bank Protection Measures” (Transp. Resour. Board 2016) gives the following data on x = shear stress (lb/ft²) and y = erosion depth (ft) for six experimental test trays at Colorado State University, built to re-create real stream conditions.

a. Construct a scatterplot. Does the simple linear regression model appear to be plausible?
b. Carry out a test of model utility.
c. Estimate true average erosion depth when shear stress is 1.75 lb/ft² by giving an interval of plausible values.
d. Estimate erosion depth along a single stream where water flow creates a shear stress of 1.75 lb/ft² by giving an interval of plausible values.

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X y 0.75 .01 1.50 .06 1.70 .10 1.61 .03 2.43 .13 3.24 .24