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e level (denoted as 'x') of 20 surveyed households. The straight line on the plot, with an on y = x + a, represents the mathematical model representing the relationship between nd income level based on the collected data by least square estimation. 16 y = Bx + α 14 12 ε₁ = y₁ - y₁ 10 6 4 2 0 20000 Trips 10000 15000 0 5000 25000 Income erpret the physical meaning of &, a and ß in the figure. scribe in detail the least square estimation method (with use of appropriate mathematical notations) with which the optimal values of a and ß can be determined.

e level (denoted as 'x') of 20 surveyed households. The straight line on the plot, with an on y = x + a, represents the mathematical model representing the relationship between nd income level based on the collected data by least square estimation. 16 y = Bx + α 14 12 ε₁ = y₁ - y₁ 10 6 4 2 0 20000 Trips 10000 15000 0 5000 25000 Income erpret the physical meaning of &, a and ß in the figure. scribe in detail the least square estimation method (with use of appropriate mathematical notations) with which the optimal values of a and ß can be determined.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 76E
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Question 2 The figure below plots the number of trips (denoted as 'y') generated against the associated income level (denoted as 'x') of 20 surveyed households. The straight line on the plot, with an equation y = 3x + a, represents the mathematical model representing the relationship between trips and income level based on the collected data by least square estimation. 16 y = Bx + α 14 12 ε₁ = y₁ - y₁ 10 8 6 4 2 0 10000 20000 Trips 0 5000 15000 25000 Income a) Interpret the physical meaning of ɛ, a and ß in the figure. b) Describe in detail the least square estimation method (with use of appropriate mathematical notations) with which the optimal values of a and ß can be determined.
Transcribed Image Text:Question 2 The figure below plots the number of trips (denoted as 'y') generated against the associated income level (denoted as 'x') of 20 surveyed households. The straight line on the plot, with an equation y = 3x + a, represents the mathematical model representing the relationship between trips and income level based on the collected data by least square estimation. 16 y = Bx + α 14 12 ε₁ = y₁ - y₁ 10 8 6 4 2 0 10000 20000 Trips 0 5000 15000 25000 Income a) Interpret the physical meaning of ɛ, a and ß in the figure. b) Describe in detail the least square estimation method (with use of appropriate mathematical notations) with which the optimal values of a and ß can be determined.
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