Engineering Structures (July 2013) published a study of the characteristics of fresh concrete. One key variable studied was the time (in hours) needed for pressure stabilization of the concrete. The researchers investigated the effect of time needed for pressure stabilization (x) on each of three different dependent variables: y₁ = initial setting time (hours), y₂ = final setting time (hours), and y₃ = maturity index (ºC-hours). The data on these variables for n = 8 fresh concrete lateral pressure tests are listed in the table.

a. Construct scatter grams to aid the researchers in determining whether pressure stabilization can be used as a reliable predictor of any of the three dependent variables.

b. Support your answer to part a by running three simple linear regression analyses. Are any of the slopes significantly different from 0? (Test using α = .05.) Which one?

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CONCRET2 Test Y1 Y2 Y3 X Al 4.63 7.17 385.81 12.03 A2 4.32 6.52 358.44 11.32 A3 4.54 6.31 292.71 9.51 A4 4.09 6.19 253.16 8.25 A5 4.56 6.81 279.82 9.02 A6 4.48 6.98 318.74 9.97 A7 4.35 6.45 262.14 8.42 A8 4.23 6.69 244.97 7.53