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Describe the number of points that simultaneously lie in each of the three planes shown

Elementary Linear Algebra with Applications | 9th Edition | ISBN: 9780132296540 | Authors: Bernard Kolman David Hill ISBN: 9780132296540 301

Solution for problem 26 Chapter 1.1

Elementary Linear Algebra with Applications | 9th Edition

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Elementary Linear Algebra with Applications | 9th Edition | ISBN: 9780132296540 | Authors: Bernard Kolman David Hill

Elementary Linear Algebra with Applications | 9th Edition

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Problem 26

Describe the number of points that simultaneously lie in each of the three planes shown in each part of Figure 1.2.

Step-by-Step Solution:
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Linear Regression Mathematical Models  Expression that describes the relationship between variables  2 types o Deterministic model o Probabilistic model  Hypothesize 2 components  Deterministic  Random error Straight line probabilistic model y =  0+  x1+ y  dependent variable x  independent variable E(y) = 0 + 1x  Deterministic component  (epsilon)  Random error component  0(beta zero) = y­intercept of the line  1(beta one) = slope of the line How do you determine what line “fits best” on a Scattergram Least Squares line  Sum of the errors = 0 o Mean error = 0  Sum of squared errors (SSE) is smaller than for any other straight­line model o Error variance is minimum How to determine the line: Finding it on the Calculator: Input the data given (STAT, Edit) Finding line  STAT, CALC, LinReg LinReg will automatically have L1 as the x values and L2 as the y values Example You’re a marketing analyst for Hasbro Toys. You gather the following data: Ad Expenditure (100$) Sales (Units) 1 1 2 1 3 2 4 2 5 4 Find the least squares line relating sales and advertising. Basic Assumptions of Probability Distribution:

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Chapter 1.1, Problem 26 is Solved
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Textbook: Elementary Linear Algebra with Applications
Edition: 9
Author: Bernard Kolman David Hill
ISBN: 9780132296540

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Describe the number of points that simultaneously lie in each of the three planes shown