In StatCrunch : In mining engineering, holes are often drilled through rock, usi
ID: 3365359 • Letter: I
Question
In StatCrunch: In mining engineering, holes are often drilled through rock, using drill bits. It is expected that drilling time increases with depth. The business problem relates to whether drilling is faster using dry drilling holes or wet drilling holes. Data have been collected from a sample of drill holes that contains measurements of the time to drill each additional 5 feet (in minutes), the depth (in feet), and whether the hole was dry or wet. Use the data given below to complete parts (a) through (g). For parts (a) through (d), do not include an interaction term.
Depth Time Type
5 4.76 dry
10 4.88 dry
15 6.55 dry
20 6.53 dry
25 6.86 dry
30 7.30 dry
35 5.86 dry
40 6.92 dry
45 5.32 dry
50 5.92 dry
55 6.06 dry
60 6.25 dry
65 6.16 dry
70 5.82 dry
75 6.17 dry
80 5.45 dry
85 5.55 dry
90 6.04 dry
95 6.47 dry
100 5.68 dry
105 5.06 dry
110 5.91 dry
115 6.63 dry
120 6.36 dry
125 6.91 dry
130 6.70 dry
135 7.17 dry
140 6.71 dry
145 6.98 dry
150 7.11 dry
155 6.89 dry
160 6.77 dry
165 6.55 dry
170 5.79 dry
175 7.61 dry
180 6.98 dry
185 6.88 dry
190 6.97 dry
195 6.74 dry
200 6.01 dry
205 6.07 dry
210 6.10 dry
215 5.43 dry
220 7.05 dry
225 7.44 dry
230 8.13 dry
235 7.39 dry
240 6.27 dry
245 6.92 dry
250 6.42 dry
5 8.80 wet
10 7.83 wet
15 7.15 wet
20 8.44 wet
25 9.29 wet
30 9.95 wet
35 8.63 wet
40 7.61 wet
45 8.20 wet
50 7.39 wet
55 8.07 wet
60 8.83 wet
65 9.12 wet
70 9.08 wet
75 8.51 wet
80 9.08 wet
85 9.04 wet
90 9.18 wet
95 8.64 wet
100 8.72 wet
105 8.20 wet
110 7.22 wet
115 7.97 wet
120 7.90 wet
125 7.99 wet
130 8.43 wet
135 9.16 wet
140 9.34 wet
145 9.16 wet
150 8.86 wet
155 8.62 wet
160 9.23 wet
165 6.93 wet
170 8.92 wet
175 9.28 wet
180 8.77 wet
185 8.06 wet
190 8.49 wet
195 9.53 wet
200 10.68 wet
205 10.30 wet
210 9.17 wet
215 9.13 wet
220 10.26 wet
225 11.13 wet
230 8.82 wet
235 9.20 wet
240 10.16 wet
245 11.38 wet
250 8.03 wet
a. State the multiple regression equation that predicts the time, based on the depth, X1, and the type, X2.
Define X2 to be 0 for dry drilling holes and let X2 be 1 for wet drilling holes.
(Round to three decimal places as needed.) b. Interpret the regression coefficients in (a) Holding constant whether the drilling hole is dry or wet, for each increase of 1 is the depth of the hole, the predicted time is estimated to increase by inutes. Holding constant the depth of the hole minutes over the the drilling hole being "wet or drv is estimated to increase the time by time it would take to drill a "wet or dry hole (Round to three decimal places as needed.) c. At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model Test the first independent variable, Depth. Determine the null and alternative hypotheses -l The test statistic for the first independent variable, Depth, is t STAT (Round to three decimal places as needed.) The p-value for the first independent variable, Depth, i (Round to four decimal places as needed.) Since the p-value is less/greater" than the value of , "reject do not relect the null hypothesis. The first independent variable, Depth, "does not appear appears" to make a contribution to the regression model Test the second independent variable, Type. Determine the null and alternative hypotheses. d. Construct and interpret a 95% confidence interval estimate of the population slope of the relationship between Time and Depth Taking into account the effect of "Depth Time, Type" the estimated effect of Depth increasing by 1 foot is to change the "Depth, Time, Type" by minutes (Round to three decimal places as needed. Use ascending order.) e. Construct and interpret a 95% confidence interval estimate of the population slope of the relationship between Time and Type. Taking into account the effect of Depth, Time, Type" the estimated effect of Depth increasing by 1 foot isExplanation / Answer
a) The regression equation is
Time Y-cap = 8.18 + 0.00518 Depth(x1) - 2.43 Type_dry(x2)
b) 0.00518 and -2.43
c) H0: beta1 = 0
H1: beta1 not = 0
d) P-value = 0.000
since p-vlaue is less than the alpha, reject the null hypothesis. The first independent variable, Depeth, appears to make a contribution to the regression model,
d) The 95% confdience interval estimtae of the population slope (7.8453, 8.5189) minutes
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