Linear least squares Consider the relation between hours of study and quiz grade for three different students. -- Student 1 did not spend any time and received 5 in the quiz. P : (0, 5) Student 2 spent an hour studying and received 5 in the quiz. P2 = (1, 5) -- -- Student 3 spent two hours studying and received 8 in the quiz. P3 = (2, 8). We want to find a linear relation between hours of study and grade of the quiz y = mx + q where m and q are our unknowns, x represents the hours studied for the quiz and y the quiz grade.
Linear least squares Consider the relation between hours of study and quiz grade for three different students. -- Student 1 did not spend any time and received 5 in the quiz. P : (0, 5) Student 2 spent an hour studying and received 5 in the quiz. P2 = (1, 5) -- -- Student 3 spent two hours studying and received 8 in the quiz. P3 = (2, 8). We want to find a linear relation between hours of study and grade of the quiz y = mx + q where m and q are our unknowns, x represents the hours studied for the quiz and y the quiz grade.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:Theorem 3.26: Determinant of the Transpose
Let A be a matrix where A" is the transpose of A. Then,
det (A") = det (A)
Theorem 3.28: Determinant of the Inverse
Let A be an n x n matrix. Then A is invertible if and only if det(A) 0. If this is true, it follows that
1
det(A¬1)
det(A)
Transcribed Image Text:Linear least squares
Consider the relation between hours of study and quiz grade for three different students.
- Student 1 did not spend any time and received 5 in the quiz. Pı = (0, 5)
--
- Student 2 spent an hour studying and received 5 in the quiz. P2 = (1, 5)
--
- Student 3 spent two hours studying and received 8 in the quiz. P3 = (2, 8)..
--
We want to find a linear relation between hours of study and grade of the quiz y =
mx + q where m
and q are our unknowns, x represents the hours studied for the quiz and y the quiz grade.
(c) Compute (A?A)-! using the determinant formula in Chapter 3.2 of the Kuttler textbook.
(d) Compute x =
(AT A)-ATb and find m = x1 and q = x2.
(e) Plot the line obtained by replacing m and q and the points P1 , P2 and P3 .
- What do you
observe? In what way is this line a good representative of the data. This method is called least-square
estimation and can be applied to larger sets of points.
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