GLM 2- Multiple Regression Flashcards
What is a polynomial regression?
A statistical method of determining the relationship between an independent variable (x) and a dependent variable (y) and model their relationship as the nth degree polynomial.
When is a polynomial regression used?
When the relationship between two variables is non-linear.
How can a simple regression of Y onto 1 predictor, X1 be written?
Y = β0 + β1X1 + ε,
where recall that ε is the error term.
How can a simple regression of Y onto 1 predictor, X1 be written?
Y = β0 + β1X1 + ε,
where recall that ε is the error term.
Uppercase Y = random variable y
Multiple regression still involves single intercept B0 which is the value taken by Y when all x’s are set to 0
How are the estimated parameters of a multiple regression of Y onto X1, . . . , Xp given by?
Y^i = B^0 +B^1xi1 + B6
For a simple regression, parameters B0 and B1 determine equation for a line. What do they determine in multiple regression?
Hyperplane
What is a matrix X an arranged arrangement of?
(X)ij = xij
A matrix X is of what order?
r x c
It has r rows and c columns with i = 1 (row) and j = 1 (column)
How can a matrix be visualised
As a spreadsheet of numbers with rows r and columns c
What are vectors?
Special cases of matrices in which one of the dimensions is 1
What is a column vector?
A matrix of order (r x1)
What is a row vector?
Matrix of order (1xc)
What is a scalar or element?
Matrix of order (1x1)
Scalars are entries in matrix, denoted by non bold letter
All symmetric matrices are what?
Square
A matrix is said to be square if what?
r = c.
A matrix is symmetric, if what?
xij = xji , for all i = 1, . . . , r , and j = 1, . . . , c.
What matrix is non standardised?
Covariance
What matrix is standardised?
Correlation
A square matrix is diagonal if what?
If xij = 0, for every i /= j.
The diagonal matrix, whose diagonal elements are 1’s is the identity matrix, and is denoted as what?
In (I is bold)
The multivariate mean is also what?
A p-dimensional column vector, ¯x.
¯x = x1 + x2 + . . . + xn.
The multivariate mean is also what?
A p-dimensional column vector, ¯x.
¯x = x1 + x2 + . . . + xn.
Vectors are treated as numbers as long as what?
They have the same dimensions
How is matrix addition applied?
Elementwise, or element by element.
How is matrix subtraction applied?
Elementwise, or element by element.
To transpose a matrix is to what?
Invert its dimensions.
The transpose of a matrix A of order r × c is the matrix what?
AT of order c × r
with (AT )ij = (A)ji.
for every i = 1, . . . , r and j = 1, . . . , c.
Transposition is so common that the command in R is just..
t(A) for some matrix A.
