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Consider the relation between hours * of study and quiz grade for three different students. (i) Student 1 did not spend any time and received 5 in the quiz. P = (0, 5) (ii) Student 2 spent an hour studying and received 5 in the quiz. P2 = (1, 5) (iii) 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. (4a, Show that there is no line y = mx + q that passes through P1, P and P3 using an inconsistent system of equations. Hint: Substitute the x and y values of P1, P2, P3 in the line equation and show that the 3x2 system with unknowns m and q has no solutions. (4b, Write the system of equations for part a) in matrix form Ax = b where i = (m, q)" . (4c, Compute (AT A)-1. (4d, * = (A" A)-' A™b and find m = x1 Compute and q = x2. (4е, Plot the line obtained by replacing m and q and the points P1 , P2 and P3 Optional - What do you observe? In what way is this line a good representative of the data.

Consider the relation between hours * of study and quiz grade for three different students. (i) Student 1 did not spend any time and received 5 in the quiz. P = (0, 5) (ii) Student 2 spent an hour studying and received 5 in the quiz. P2 = (1, 5) (iii) 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. (4a, Show that there is no line y = mx + q that passes through P1, P and P3 using an inconsistent system of equations. Hint: Substitute the x and y values of P1, P2, P3 in the line equation and show that the 3x2 system with unknowns m and q has no solutions. (4b, Write the system of equations for part a) in matrix form Ax = b where i = (m, q)" . (4c, Compute (AT A)-1. (4d, * = (A" A)-' A™b and find m = x1 Compute and q = x2. (4е, Plot the line obtained by replacing m and q and the points P1 , P2 and P3 Optional - What do you observe? In what way is this line a good representative of the data.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...
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O Consider the relation between hours 4: of study and quiz grade for three different students. (i) Student 1 did not spend any time and received 5 in the quiz. P = (0, 5) (ii) Student 2 spent an hour studying and received 5 in the quiz. P2 = (1, 5) (iii) 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. (4a, Show that there is no line y — mх + that passes through P1 , P and P3 using an inconsistent system of equations. Hint: Substitute the x and y values of P1, P2, P3 in the line equation and show that the 3x2 system with unknowns m and q has no solutions. (4b, Write the system of equations for part a) in matrix form Ax = b where i = (m, q)' . (4с, Compute (A" A)-1. (4d, Compute * = (AT A)- A" b and find m = x1 and q = x2· (4e, Plot the line obtained by replacing m and q and the points P1, P and P3 Optional - What do you observe? In what way is this line a good representative of the data.
Transcribed Image Text:O Consider the relation between hours 4: of study and quiz grade for three different students. (i) Student 1 did not spend any time and received 5 in the quiz. P = (0, 5) (ii) Student 2 spent an hour studying and received 5 in the quiz. P2 = (1, 5) (iii) 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. (4a, Show that there is no line y — mх + that passes through P1 , P and P3 using an inconsistent system of equations. Hint: Substitute the x and y values of P1, P2, P3 in the line equation and show that the 3x2 system with unknowns m and q has no solutions. (4b, Write the system of equations for part a) in matrix form Ax = b where i = (m, q)' . (4с, Compute (A" A)-1. (4d, Compute * = (AT A)- A" b and find m = x1 and q = x2· (4e, Plot the line obtained by replacing m and q and the points P1, P and P3 Optional - What do you observe? In what way is this line a good representative of the data.
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