Compute the linear correlation coefficient between the two variables and determine whether a linear relation exists. x -1       1    8    5    3    2      4   6   7    0 y -13   -11   6    -2   -5   -9   -4   0    3  -11 a. r = 0.990; linear relation exists b. r = 0.819; linear relation exists c. r = 0.792; no linear relation exists d. r = 0.881; no linear relation exists

Which of the following sets are linearly dependent? Select all possible answers. 3 9 4 12 |} 3 -2 { 2 1 } 3 1 21 { -14 } 7 000 0000 { } -3 7 4 { 2 -2 } -3

Do question 4 only

Plot the scatter plot defined by the points on the left. Then match it to the correct correlation value. {(1, 3), (1, 8), (5, 9), (8, 3), (8, 8)} {(1, 4), (3, 3), (5, 7), (7, 5), (9, 8)} r = 0.03 r = -1

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. (a) Show that there is no line y = mx + q that passes through Pi , P2 and P3 using an inconsistent system of equations. Hint: Substitute the x and y values of P1, P,, P3 in the line equation and show that the 3x2 system with unknowns m and q has no solutions. (b) Write the system of equations for part a) in matrix form Ax = b where x = (m, q)" . (c) Compute (A' A)¯ using the determinant formula in Chapter 3.2 of the Kuttler textbook. (d) Compute x = (A" A)~!A" b and…

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). %3| 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. (4а Show that there is no line y = mx + q that passes through P , P and P3 using an inconsistent system of equations. Hint: Substitute the x and y values of P, P, P3 in the line equation and show that the 3x2 system with unknowns m and g has no solutions. (4b Write the system of equations for part a) in matrix form Aš b where i = (m, q)" . (4c Compute (AT A)-1. (4d Compute i (AT A)-' A™ b and find m = x1 and q = x2. (4e Plot the line obtained by replacing m and q and the…