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In order to increase the production of gas wells, a procedure known as hydraulic fracturing is often used. Fracture fluid, which consists of fluid mixed with sand, is pumped into the well. The following figure presents a scatterplot of the monthly production versus the volume of fracture fluid pumped for 255 gas wells. Both production and fluid are expressed in units of volume per foot of depth of the well. The least-squares line is superimposed. The equation of the least-squares line is y = 106.11 + 0.1119x. 1600 1400 1200- 1000 - 800 F 600F 400 200 2000 4000 6000 8000 Fracture fluid (gnl/ft) From the least-squares line, estimate the production for a well into which 4000 gal/ft are pumped. From the least-squares line, estimate the production for a well into which 500 gal/ft are pumped. A new well is dug, and 500 gal/ft of fracture fluid are pumped in. Based on the scatterplot, is it more likely that the production of this well will fall above or below the least-squares estimate? d. What feature of the scatterplot indicates that assumption 3 on page 549 is violated? a. b. c. Prodaction (1000 ft Vfr)

In order to increase the production of gas wells, a procedure known as hydraulic fracturing is often used. Fracture fluid, which consists of fluid mixed with sand, is pumped into the well. The following figure presents a scatterplot of the monthly production versus the volume of fracture fluid pumped for 255 gas wells. Both production and fluid are expressed in units of volume per foot of depth of the well. The least-squares line is superimposed. The equation of the least-squares line is y = 106.11 + 0.1119x. 1600 1400 1200- 1000 - 800 F 600F 400 200 2000 4000 6000 8000 Fracture fluid (gnl/ft) From the least-squares line, estimate the production for a well into which 4000 gal/ft are pumped. From the least-squares line, estimate the production for a well into which 500 gal/ft are pumped. A new well is dug, and 500 gal/ft of fracture fluid are pumped in. Based on the scatterplot, is it more likely that the production of this well will fall above or below the least-squares estimate? d. What feature of the scatterplot indicates that assumption 3 on page 549 is violated? a. b. c. Prodaction (1000 ft Vfr)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 34EQ
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In order to increase the production of gas wells, a procedure known as hydraulic fracturing is often used. Fracture fluid, which consists of fluid mixed with sand, is pumped into the well. The following figure presents a scatterplot of the monthly production versus the volume of fracture fluid pumped for 255 gas wells. Both production and fluid are expressed in units of volume per foot of depth of the well. The least-squares line is superimposed. The equation of the least-squares line is y = 106.11 + 0.1119x. 1600 1400 1200- 1000 - 800 F 600F 400 200 2000 4000 6000 8000 Fracture fluid (gnl/ft) From the least-squares line, estimate the production for a well into which 4000 gal/ft are pumped. From the least-squares line, estimate the production for a well into which 500 gal/ft are pumped. A new well is dug, and 500 gal/ft of fracture fluid are pumped in. Based on the scatterplot, is it more likely that the production of this well will fall above or below the least-squares estimate? d. What feature of the scatterplot indicates that assumption 3 on page 549 is violated? a. b. c. Prodaction (1000 ft Vfr)
Transcribed Image Text:In order to increase the production of gas wells, a procedure known as hydraulic fracturing is often used. Fracture fluid, which consists of fluid mixed with sand, is pumped into the well. The following figure presents a scatterplot of the monthly production versus the volume of fracture fluid pumped for 255 gas wells. Both production and fluid are expressed in units of volume per foot of depth of the well. The least-squares line is superimposed. The equation of the least-squares line is y = 106.11 + 0.1119x. 1600 1400 1200- 1000 - 800 F 600F 400 200 2000 4000 6000 8000 Fracture fluid (gnl/ft) From the least-squares line, estimate the production for a well into which 4000 gal/ft are pumped. From the least-squares line, estimate the production for a well into which 500 gal/ft are pumped. A new well is dug, and 500 gal/ft of fracture fluid are pumped in. Based on the scatterplot, is it more likely that the production of this well will fall above or below the least-squares estimate? d. What feature of the scatterplot indicates that assumption 3 on page 549 is violated? a. b. c. Prodaction (1000 ft Vfr)
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