Formula Sheet
Formula Sheet
Chapter 2
Expected Value of a Discrete Random Variable (a.k.a. mean):
[pic]
The expected value of a function of a discrete random variable X:
[pic]
The variance of a discrete random variable X:
[pic]
but also, [pic]
Standard Deviation [pic]
Rules of Expectation: where a and c are constants and X is a random variable
[pic]
Rules of Variance:
[pic]
Conditional Probability:
[pic] where f(X,Y) is the joint probability
Covariance:
[pic]
but also [pic]
where [pic]
Correlation: [pic]
The sum of two random variables: Let X and Y be two random variables and a and b are constants:
E(aX + bY) = aE(X) + bE(Y)
Var(aX + bY) = a2Var(X) + b2Var(Y) + 2abCov(X,Y)
Sample Statistics: assume a sample of T observation on Xt
Sample Mean
Sample Variance
Sample Standard Deviation
Sample Covariance
Sample Correlation
Chapter 3 and 4 Formulas The Method of Least Squares
For the linear model : [pic], the Least Squares estimator is comprised of the following 2 formulas (where T is the size of the sample):
[pic]
[pic]
Note that b2 could also be calculated using one of the other 3 formulas:
[pic]
[pic]
[pic] where [pic]
These estimators have the following means and variances:
[pic] and [pic]
[pic] and [pic]
[pic]
where (2 is the variance of the error term and is assumed constant.
The estimated line is: [pic] and a residual is [pic]
The estimator of (2 is [pic] so that
[pic] and [pic]where a “hat” means that [pic] has been used in place of (2 in the variance formulas.
Chapter 5 and 6 Equations
From Section 5.3: The Least squares predictor uses the estimated model to make a prediction at xo.
The estimated variance of the prediction error is:
R-squared is:
where
So that
Chapter 7 and 8
For the multiple regression model:
Adjusted R-squared:
F-statistic:
Let SSER be the sum of squared residuals from the Restricted Model
Let SSEU be the sum of squared residuals from the Unrestricted Model.
Let J be the number of “restrictions” that are placed on the Unrestricted
model in constructing the Restricted model. Let T be the number of observations in the data set. Let k be the number of RHS variables plus one for intercept in the
Unrestricted model.
Chapter 11
Goldfeld Quandt statistic:
This statistic has an F distribution with t1-k degrees of freedom in the numerator and t2-k degrees of freedom in the denominator
The variance for b2 when the error term is heteroskedastic is:
White standard errors use this Var(b2) formula, using [pic]as an estimate for [pic].
Chapter 12
Durbin-Watson test statistic is calculated as:
and
-----------------------
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
[pic]
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- formula sheet for statistics pdf
- statistics formula sheet with explanation
- derivative formula sheet pdf
- trig identities formula sheet pdf
- ged math formula sheet 2019
- mathematics formula sheet ged
- formula sheet for ged
- ged formula sheet 2017
- ged formula sheet printable pdf
- electrical formula sheet pdf
- differential equations formula sheet pdf
- ged formula sheet pdf