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.
