LEVEL II Leverage measures how far an observation is from the average value of the independent variable. High leverage observations are those that are far away from the average and have a large effect on the regression line. For a particular independent variable, leverage of a particular data point measures the distance between its value and the mean value of …
Influence Analysis
LEVEL II In regression analysis, influence analysis is a method used to identify which observations in a dataset have a disproportionate effect on the estimated regression coefficients. This can help to identify outliers or observations that are having a large effect on the overall regression model. There are several measures that can be used to determine the influence of an …
Variance Inflation Factor [VIF]
LEVEL II The Variance Inflation Factor (VIF) is a measure of how much the variance of an estimated regression coefficient is increased due to multicollinearity in the model. It is used to identify correlated independent variables in a multiple regression model. We start by regressing each of the independent variables against the remaining independent variables. The R-squared from the regression …
Multicollinearity
Multicollinearity occurs when two or more independent variables in a multiple regression model are highly correlated with each other. This can create problems when interpreting the regression coefficients, as the estimated coefficients of the correlated variables can change erratically in response to small changes in the data or the model. There are several ways to detect multicollinearity in a regression …
Breusch-Godfrey test [BG Test]
LEVEL II The Breusch-Godfrey test is a statistical test that is used to detect autocorrelation in the residuals of a linear regression model. It helps to detect autocorrelation at different lags and it’s applicable to both linear and non-linear models. The test starts with an initial regression where we record down all the residuals for each time period. The residual …
Durbin-Watson Test [DW Test]
LEVEL II The Durbin-Watson (DW) test is a statistical test used to detect autocorrelation in the residuals of a linear regression model. The test statistic is a value between 0 and 4, with the null hypothesis being that there is no autocorrelation in the residuals. A value close to 2 indicates no autocorrelation, a value less than 2 indicates positive …
Serial Correlation
LEVEL II Autocorrelation is the correlation of a time series with a lagged version of itself. It measures the similarity between a given time series and a lagged version of the same time series. Positive autocorrelation means that the time series is positively correlated with a lagged version of itself, while negative autocorrelation means that the time series is negatively …
Breusch-Pagan Test [BP Test]
LEVEL II The Breusch-Pagan test is a statistical test used to detect the presence of heteroskedasticity in a linear regression model. It is based on the idea that if heteroskedasticity is present, the variance of the error term should be related to the predictor variables in the model. The test involves regressing the squared residuals of the original regression model …
Heteroskedasticity
LEVEL II Heteroskedasticity refers to the situation where the variance of the error term in a statistical model is not constant across all values of the predictor variables. This can lead to inaccurate results and invalid conclusions in the model. There are two types of heteroskedasticity: unconditional and conditional. Unconditional heteroskedasticity occurs when the variance of the error term is …
Joint hypothesis test
LEVEL II A joint hypothesis test is an F-test to evaluate nested models, which consist of a full or unrestricted model, and a restricted model. The F-statistic is calculated using the formula shown. The null hypothesis would be that all coefficients of the excluded variables are equal to zero, and the null that at least one of the excluded coefficients …