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Math / Linear Algebra: A Geometric Approach 2 / Chapter 4.1 / Problem 10

Linear Algebra: A Geometric Approach | 2nd Edition | ISBN: 9781429215213 | Authors: Ted Shifrin, Malcolm Adams

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Consider the four data points (1, 1), (2, 2), (3, 1), (4, 3). a. Find the least squares

Chapter 4, Problem 10

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QUESTION:

Consider the four data points (1,1),(2,2),(3,1),(4,3).

a. Find the "least squares horizontal line" y = a fitting the data points. Check that the sum of the errors is 0.

b. Find the "least squares line" y = ax + b fitting the data points. Check that the sum of the errors is 0 .

c. (Calculator recommended) Find the "least squares parabola" \(y=a x^2+b x+c\) fitting the data points. What is true of the sum of the errors in this case?

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QUESTION:

Consider the four data points (1,1),(2,2),(3,1),(4,3).

a. Find the "least squares horizontal line" y = a fitting the data points. Check that the sum of the errors is 0.

b. Find the "least squares line" y = ax + b fitting the data points. Check that the sum of the errors is 0 .

c. (Calculator recommended) Find the "least squares parabola" \(y=a x^2+b x+c\) fitting the data points. What is true of the sum of the errors in this case?

ANSWER:

Step 1 of 9

a) To find the “least squares horizontal line” fitting the data point

We get the system of equations as,

Which in matrix form becomes,

We get,

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