Pillar stability is a most important factor to ensure safe conditions in underground mines. The authors of "Developing Coal Pillar Stability Chart Using Logistic Regression" (Intl. J. of Rock Mechanics & Mining Sci., 2013: 55-60) used a logistic regression model to predict stability. The article reported the following data on x1 = pillar height to width ratio, x2 = pillar strength to stress ratio, and stability status for 29 coal pillars.

The corresponding logistic regression output from R is given here:

a. Using the output with α = .1 to determine whether the two predictor variables appear to have a significant impact on pillar stability.
b. Provide interpretations for e and e5.668.

ID 2 Stable?IDStable? 1 1.80 2.40 Y 2 1.65 2.54 3 2.70 0.84 Y 4 3.67 168Y 6 0.80 1.37 N 17 0.60 1.27 18 1.30 0.87 N 19 0.83 0.97 N 1.41 241 Y20 0.57 0.94 N 6 1.76 193Y 7 2.10 1.77 Y 22 2.08 0.78 N 8 2.10 1.50Y23 150 103 N 9 457 2.43 Y 10 3.59 5.55Y25 094 1.30 11 8.33 2.58 Y 12 2.86 2.00Y 13 2.58 3.68 Y 21 144 1.00 N 1.03 N 24 1.38 0.82 N 26 158 0.83 N 27 1.67 1.05 N 28 3.00 119 N 29 2.21 0.86 8 14 290 113 29 221 6N 15 3.89 2.4 Coefficients: Estimate Std. Error z value Prz (Intercept)-13.146 xl I2 5.194 -2.536 0.0112 1.477 1.878 2.642 2.145 0.0319 2774 0.0604 5.669