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Test for correlation significance

Estimated slope coefficient in simple linear regression

Estimated intercept in simple linear regression

Standard Error of Estimate: definition and formula
Measures the degree of variability of the actual yvalues relative to the estimated yvalues from a regression equation. Gauges the "fit" of the line. Smaller is better

Heteroskedacity
1. What is it
2. Problem it causes
3. How to detect it
4. How to correct it
1. Error variance is nonconstant. Unconditional (variance does not correlate with x) is ok, conditional (ex. variance grows with x value) is not ok.
2. False significance of independent variables
 3. Detect with BreuschPagan test.
 where = Rsquare from second regression of squared residuals resulting from original regression. One tail test, significance means there is a problem with heteroskedacity
4. Correct with Whitecorrected standard errors

Serial correlation
1. What is it
2. Problem it causes
3. How to detect it
4. How to correct it
 aka Autocorrelation
 1. Residual terms are correlated (ie if one is positive, the next is positive)
2. False significance of independent variables
 3. Detect with DurbinWatson test.
 where = correlation coefficient between residuals from one period and those from the previous period. Use DW table to find dl and du using n and k. 3 situations:
 dtest < dl > reject null, conclude positive autocorrelation;
 dl < dtest < du > inconclusive;
 du < dtest > do not reject null, no autocorrelation
4. Hansen method

Multicollinearity
1. What is it
2. Problem it causes
3. How to detect it
4. How to correct it
1. High correlation among one or more independent variables
 2. False insignificance of independent variables

 3. Ftest is very significant, but all or many of the independent variables are not significant
4. Remove one or more of the related variables

Possible Misspecifications
 Functional
 1. Omitting important independent variable
 2. Independent variable should be transformed
 3. Incorrectly pooling data
 Correlation Between error and X
 1. x variable is lagged y variable
 2. Forecast the past  use data from end of period to forecast what happened during the same period
 3. Measurement error

How to regress qualitative dependent variables (3 models)
Can't use OLS (ordinary least squares) model, which is the regular regression model
Can use logit model, probit model, or discriminant model

Covariance Stationarity
1. What is it
2. How to determine if it exists
1. mean and variance don't change over time
2. plot data, run AR model and test correlations, perform Dickey Fuller test

Unit root
1. What is it and what does it mean
2. How to correct it
1. Coefficient on lagged dep variable = 1. Means series is not covariance stationary
2. Correct with first differencing: instead of lagged values, use difference between current value and previous value as independent variable.

Mean reverting level
 b1 < 1 is good
 b1 = 1 means unit root
 b1 > 1 means explosive data

ARCH
1. What is it
2. How to detect it
3. How to correct it
1. Autoregressive conditional heteroskedacity  cond. heteroskedacity in an AR model
2. Square residuals from original model and regress against one period lag of squared residuals. If correlation is significant, then ARCH is a problem
3. Generalized least squares model. Also, ARCH test can be used to predict future variability (NBD)

Covariance stationarity in multiple time series regression
If both indep variables are cov stationary, then good to go
If one indep variable is cov stationary but other is not, then model is no good
If both indep variables are not cov stationary, check for cointegration. If cointegrated, then good, if not, then model is no good

