What are the two most popular methods for building a SRF?
- Ordinal least squares
- Maximum Likelyhood
Why not get an SRF by minimizing Sum(u^)?
Because negative residuals will cancel out positive residuals
What is the least squares criterion?
Minimizing the summed square of the errors
How is beta two calculated in the least squares method?
How is beta one calculated?
What are the Gaussian, standard or classical linear regression model (CLRM) model assumptions?
1. The regression model is linear in the parameters
2. Xi not correlated with the error term
3. Zero mean value of error term
4. Homoscedasticity - constant error term variance for all X
5. No auto-correlation in error terms
6. The number of observations must be greater than the explanatory variables
7. Var(X) != 0
Give the formula of Var(b^2)
Give the formula of Var(b^1)
Give the formula for Var(u^i)
How is the conditional variance of ui & Yi related?
They are the same
What is the standard deviation of ui and Yi called?
The standard error of the estimate / regression
How are b1^ and b2^ related?
With positive Mean(X), overestimate of B2 will underestimate of B1,
With negative Mean(X), overestimate of B2 will overestimate B1
What is a best linear unbiased estimator (BLUE) ?
An estimator where: 1. Linear 2. Unbiased 3. Least variance of all same class estimators.
What does the Guauss-Markov theorem state?
Given the assumptions of CLRM, the least squares estimates are BLUE
What is the coefficient of the determinant
A measure of the goodness of the fit, of a regression line to a sample - signified as r^2 for the two variable case and R^2 for multivariable.
How is the coefficient of determination calculated?
By considering the sum of squares, including
Total sum of squares (TSS)
Explained sum of squares (ESS)
And residual or unexplained sum of squares (RSS)
What is the coefficient of correlation?
r = sqr(r^2), can be -1 < r < 1, and matches the sign of b2^
What decreases variation of b2^?
- Xi close to zero - Large n - Low sample variance
What decreases variation of B2^
- Large variation in Xi - Large n - Low sample variance