| Notation | Definition |
|---|---|
| SLR | Simple linear regression model yi=b0+b1xi+ei ei have E(e)=0,V(e)=sigma2, and Cov(ei,ej)=0. |
| OLS | Ordinary Least Squares |
| RSS | Residual sum of squares = |ehat|2. |
| TSS | Total sum of squares = |y|2. |
| MSS | Model (or Regression) sum of squares = TSS-RSS |
| SXX,SYY | Sums of squares of X's and Y's, respectively,
corrected for the mean. Thus, SXX = Sum(xi-xbar)2=|x*|2. |
| SXY | Corrected sum of cross products of Y and X, that is, (x*)'(y*). |
| y*,x* | The asterisk denotes correction
by subtracting the mean. Thus, x* = x - xbar 1 |
| p | The number of predictors in a multiple regression model, not including the constant term, if any. |
| p', k | The total number of predictors in a multiple
regression model. Thus, k = p+1 in standard regression models, k = p in regression through the origin models. |
| p.d. p.s.d | Positive definite (positive semidefinite): A symmetric matrix A is positive semidefinite if c'Ac >= 0, for all vectors c. If, in addition, c'Ac=0 is true only for the trivial vector c=0, then A is said to be positive definite. |
| GLS | Generalized Least Squares. The GLS model differs from the OLS model in that the errors e in Y= Xb+e have a covariance matrix proportional to a known positive definite matrix A. This permits the errors (and hence, Y) to have different variances and nonzero covariances. |
| WLS | Weighted Least Squares. The special case of the GLS model in which the errors e have a diagonal covariance matrix, known up to scale factor. |
| i.i.d., or iid |
Independent, and identically distributed. Iid random variables have the same distribution, and are stochastically independent of one another. |
| Spose, defn, indpt, ito |
Suppose Definition Independent It turns out --- These are shorthand used in the lectures |