Answered: 1. By minimizing the sum of the squares…

1. By minimizing the sum of the squares of the vertical distance between the line and the points, determine the least-squares line through the data points (1,1), (2,3) and (3,2).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy

Problem 1EA

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Question

The method of least squares

Subject: Vector Calculus

Please fill in all necessary solutions.

1. By minimizing the sum of the squares of the vertical distance between the line and the points,
determine the least-squares line through the data points (1,1), (2,3) and (3,2).

Calculus that deals with differentiation and integration of the vector field in three-dimensional Euclidean space. It deals with quantities that have both magnitude and direction.

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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. From the least-squares line, estimate the production for a well into which 4000 gal/ft are pumped. Round the answer to three decimal places.
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