Explanation Given: The given points are ( − 1 , 2 ) ( 0 , − 1 ) ( 1 , 1 ) . Concept used: Let us consider that equation of the least square line be y = b + m x . Minimize f ( b , m ) to find the value of b and m . The function f ( b , m ) will be the sum of square of the vertical distance from the given points ( x 2 , y 2 ) , ( x 2 , y 2 ) , ( x 3 , y 3 ) to the line. f ( b , m ) = ( y 1 − ( b + x 1 m ) ) 2 + ( y 2 − ( b + x 2 m ) ) 2 + ( y 3 − ( b + x 3 m ) ) 2 Calculation: Here, the given points are ( − 1 , 2 ) ( 0 , − 1 ) ( 1 , 1 ) . y 1 = 2 , y 2 = − 1 , y 3 = 1 and x 1 = − 1 , x 2 = 0 , x 3 = 1 We have the equation of the line as y = b + m x . f ( b , m ) = ( 2 − ( b − m ) ) 2 + ( − 1 − ( b + 0 ) ) 2 + ( 1 − ( b + m ) ) 2 Differentiate f ( b , m ) partially with respect to b . f b = 2 ( 2 − ( b − m ) ( − 1 ) ) + 2 ( − 1 − ( b ) ( − 1 ) ) + 2 ( 1 − ( b + m ) ( − 1 ) ) f b = − 4 + 2 b − 2 m + 2 + 2 b − 2 + 2 b + 2 m f b = − 4 + 6 b Differentiate f ( b , m ) partially with respect to m

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Chapter 8, Problem 1FOT

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To find:

The least-squares line.

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Chapter 8 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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The least-squares line.

Solution Summary: The author calculates the least-squares line using y=0.66-0.5x. The function will be the sum of square of the vertical distance from the given points.

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To find: The least-squares line.

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Chapter 8 Solutions

To find:

The least-squares line.