 158.1: Does a correlation coefficient of 21 indicate a lower degree of cor...
 158.2: If you keep a record of the temperature in degrees Fahrenheit and i...
 158.3: In 36, for each of the given scatter plots, determine whether the c...
 158.4: In 36, for each of the given scatter plots, determine whether the c...
 158.5: In 36, for each of the given scatter plots, determine whether the c...
 158.6: In 36, for each of the given scatter plots, determine whether the c...
 158.7: In 714, for each of the given correlation coefficients, describe th...
 158.8: In 714, for each of the given correlation coefficients, describe th...
 158.9: In 714, for each of the given correlation coefficients, describe th...
 158.10: In 714, for each of the given correlation coefficients, describe th...
 158.11: In 714, for each of the given correlation coefficients, describe th...
 158.12: In 714, for each of the given correlation coefficients, describe th...
 158.13: In 714, for each of the given correlation coefficients, describe th...
 158.14: In 714, for each of the given correlation coefficients, describe th...
 158.15: In 1519: a. Draw a scatter plot for each data set. b. Based on the ...
 158.16: In 1519: a. Draw a scatter plot for each data set. b. Based on the ...
 158.17: In 1519: a. Draw a scatter plot for each data set. b. Based on the ...
 158.18: In 1519: a. Draw a scatter plot for each data set. b. Based on the ...
 158.19: In 1519: a. Draw a scatter plot for each data set. b. Based on the ...
 158.20: a. In Exercises 18 and 19, if the forecasts were 100% accurate, wha...
Solutions for Chapter 158: CORRELATION COEFFICIENT
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 158: CORRELATION COEFFICIENT
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Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·