The following data represent the time (minutes) it takes to drill an additional 5 feet from the depth indicated for both wet drilling and dry drilling conditions.

(a) Draw a scatter diagram, treating depth as the explanatory variable and time as the response variable, but use a different plotting symbol for wet and dry. For example, use a circle for wet and a square for dry.
(b) Find the least-squares regression equation yÌ… = b0 + b1x1 + b2 x2, where x1 is depth and x2 = 0 for wet and x2 = 1 for dry.
(c) Test the hypotheses H0: b1 = 0 versus H1: b1 ≠ 0 and H0: b2 = 0 versus H1: b2 ≠ 0.
(d) Construct 95% confidence and prediction intervals for time to drill an additional 5 feet in dry conditions where drilling starts at 100 feet. Interpret the results.

Depth Conditions Time Depth Conditions Time 60 Wet 9.34 5 Wet 8.68 5 Wet 8.61 60 Dry 7.58 Wet 5 Dry 7.07 80 8.96 10 Wet 7.71 80 Dry 8.13 105 15 Dry 7.43 Wet 8.60 20 Wet 8.26 120 Dry 7.47 20 Dry 6.65 130 Wet 9.18 8.37 30 Wet 8.27 130 Dry 30 Dry 7.95 150 Wet 9.54 Wet 160 Dry 8.20 40 9.04 Dry 40 7.80