Kellstedt & Whitten, Chapter 9
Creating goodness-of-fit models relies on minimizing stochastic components for each case. Remember that in order to do goodness of fit, you have to eliminate negative signs, so that every stochastic component contributes to the goodness of fit, instead of cancelling each other out.
Remember: alpha = the y-intercept, and beta = the slope.
Correlation coefficients: used when both dv and iv are continuous.
When Stata says "constant," this means the y-intercept. When it says "coefficient", this means the parameter estimate, which for the dv, is the slope of the regression line. The standard error in these models is based on squaring each case's error term, finding the mean of the squares, and then taking the square root of that mean. It's called, somewhat reasonably, the "root mean-squared error."
Can also use r-squared as a goodness-of-fit measure. Divides the sum of stochastic components (squared to eliminate negative signs) by the sum of the differences between each case's DV value and mean DV value (squared to eliminate negative signs). What makes a good root MSE or r-squared depends on what the DV is, and what your theory says about it.
Why is the denominator in the unseen variance equation n-2? What does the 2 do that n-1 doesn't do?
Confidence intervals are determined by multiplying the appropriate t-statistic by the standard error for both beta and alpha.
Basic OLS assumptions: population stochastic component is normally distributed, has a mean equal to zero, and has the same variance for each case in the population. No covariance between stochastic terms of unique cases. No error in iv measurement. Model includes all necessary variables and no superfluity; model is linear and parametric (every increase in X produces the same effect in Y). DV must vary. Case count must exceed test parameters.
Why must case count exceed test parameters?