Classical Linear Regression Model Assumptions

The expected value of the error term is zero. This means that the errors are not systematically biased in either direction and average out to zero over the sample.

The variance of the error term is constant and finite. This ensures that the errors are not consistently large or small and that their spread is stable.

The covariance between any two error terms is zero. This means that the errors for different observations are not correlated, ensuring that the model adequately captures independent variations in the data.

The covariance between the error term and any explanatory variable is zero. This ensures that the errors are truly independent of the factors used to predict the dependent variable.

The error term is assumed to follow a normal distribution with a mean of zero and a constant variance. This assumption allows for the use of statistical tests and confidence intervals for the estimated coefficients.

Heteroscedasticity occurs when the variance of the error term is not constant across observations. This means the error term is wider at some points and narrower at others on the regression line.

Autocorrelation occurs when the error terms are correlated across different observations. This can happen when there is a pattern or trend in the errors, causing them to influence each other.

Violations of the assumptions of the Classical Linear Regression Model (CLRM) can lead to unreliable coefficient estimates, incorrect standard errors, and inappropriate hypothesis testing. This can significantly impact the validity and accuracy of the model results.

A statistical test that examines whether the variance of the errors in a regression model is constant across all observations. It assumes that the variance of the errors is constant (homoscedasticity).

A statistical test that examines whether the variance of the errors in a regression model changes over time. It is used to detect changes in the variance of the errors in a regression model over time.

A statistical test used to examine whether the variance of the errors in a regression model is the same across different groups or populations. It compares the variances of the errors in different groups.

A graphical method used to visualize and detect potential heteroscedasticity. It involves plotting the residuals (the differences between the actual values and the predicted values) against one of the explanatory variables.

A statistical test used to examine whether the variance of the errors in a regression model is the same across different sub-samples of data. It involves splitting the data into two or more sub-samples.

A statistical test used to examine whether the variance of the errors in a regression model is related to an observable variable. It involves regressing the squared residuals on the observable variable.

A statistical test that examines whether all the coefficients in a multiple linear regression model are simultaneously equal to zero. It is used to test the overall significance of the regression model.

A statistical test that examines whether any individual coefficient in a multiple linear regression model is statistically significant.

A statistical test that tests the null hypothesis that the regression coefficients are equal to zero. It examines whether the explanatory variables have a significant linear relationship with the dependent variable.

A statistical test that examines whether the relationship between the dependent variable and any individual explanatory variable is statistically significant.

A statistical test that examines whether the relationship between the dependent variable and all the explanatory variables is statistically significant. It is performed when multiple explanatory variables are included in the model.

The assumption that the errors in a regression model are independent of each other. It means that the error term in one observation does not affect the error term in any other observation.

The assumption that the errors in a regression model are normally distributed with a mean of zero. It helps facilitate hypothesis testing and confidence interval construction.

The assumption that the errors in a regression model have a constant variance. It implies that the variability of the predicted values remains the same across all levels of the explanatory variables.

A regression diagnostic test used to determine if any of the variables are correlated with each other, which can affect the accuracy of the regression model.

A statistical test used to examine whether the relationship between the dependent variable and the explanatory variables is linear. It is used when the linearity assumption is violated.

A statistical test that specifically addresses the assumption of homoscedasticity. It examines whether the variance of the errors changes based on any external factors or characteristics of the data.

A technique used to estimate regression coefficients when the error terms are heteroscedastic. GLS transforms the data to make the error variances equal, allowing for more efficient estimates.

A test used to determine if there is evidence of heteroscedasticity in a regression model. It involves regressing the squared residuals on the explanatory variables.

A method for correcting heteroscedasticity by transforming the data. It involves dividing each observation by a value related to the heteroscedasticity, often to make the error variances equal.

A general term used to indicate estimates of the variance of the regression coefficients that have been adjusted to account for heteroscedasticity.

A method to test for heteroscedasticity by creating a new regression using the squared residuals from the original regression. This allows for checking if the variance of errors is related to the explanatory variables.

A statistical assumption that the variance of the error term is constant across all observations. This is one of the key assumptions underlying the Classical Linear Regression Model (CLRM).

The formula used to calculate the variance of the regression coefficients. It assumes homoscedasticity, and if not, the resulting standard errors can be incorrect.

A type of regression model where the relationship between the dependent variable and the explanatory variables is assumed to be linear.

A model that assumes that the error term has a constant variance across observations.

An estimation method used to estimate the parameters of a regression model, often used when the error terms are homoscedastic. It minimizes the sum of squared residuals to obtain estimates for the coefficients.

A method for analyzing the relationship between a dependent variable and one or more independent variables. It uses statistical techniques to identify patterns and relationships in data.

A type of regression model where the relationship between the dependent variable and the explanatory variables is assumed to be non-linear.

The error term in a regression model represents the difference between the actual value of the dependent variable and the value predicted by the model. It captures the random and unexplained variations in the data.

A set of assumptions that are typically made about the error term in a regression model, including the assumption of homoscedasticity. These assumptions are crucial for the validity of the regression results.

Heteroscedasticity occurs when the variance of the error term is not constant across different observations in a regression model. This means the spread or variability of the errors changes at different points on the regression line.

Autocorrelation occurs when the error terms in a time series regression model are correlated with each other across different time periods. This means the errors exhibit a pattern or dependence on previous errors, rather than being independent.

A test for first-order autocorrelation, checking for a relationship between an error and its immediately preceding value. The Durbin-Watson test statistic is calculated using the residuals from the regression analysis.

The Durbin-Watson test statistic is a measure of autocorrelation between consecutive error terms in a time series regression model. It is calculated as the ratio of the sum of squared differences of residuals over the sum of squared residuals.

The null hypothesis of the Durbin-Watson test states that there is no autocorrelation, meaning the error terms are independent. The alternative hypothesis states that there is autocorrelation, meaning the error terms are dependent on each other.

The p-value of the Durbin-Watson test indicates the probability of observing the calculated test statistic if there were actually no autocorrelation in the data. A low p-value suggests evidence of autocorrelation.

The auxiliary regression method is used to test for heteroscedasticity in a regression model. It involves regressing the squared residuals from the original regression model on the explanatory variables from the original regression model.

The White test is a popular test for heteroscedasticity. It involves running an auxiliary regression and using the F-statistic from that regression to test if the variance of the errors is constant.

The Breusch-Pagan test, another method to detect heteroscedasticity, involves a regression of the squared residuals from the original regression model on the explanatory variables and their squares and cross-products.

Heteroscedasticity-robust standard errors are adjusted standard errors that account for the presence of heteroscedasticity in the model. They are more reliable in situations where the errors have unequal variances.

The Lagrange Multiplier (LM) test, a common heteroscedasticity test, is based on an auxiliary regression of the squared residuals on the explanatory variables.

The choice of how to handle heteroscedasticity can influence the results of a regression analysis. If heteroscedasticity is present, using heteroscedasticity-robust standard errors can improve the reliability of the estimates.

EViews, a widely used econometric software package, allows users to estimate regressions with heteroscedasticity-robust standard errors by checking the 'Heteroskedasticity consistent coefficient variance' box in the equation estimation window.

Lagged values of a variable refer to past values of that variable at different time periods. For example, the lagged value of a variable at time t-1 is its value in the previous period.

The concept of lagged values is crucial for understanding and testing for autocorrelation, especially in time series analysis. It allows us to examine the relationships between errors at different points in time.

The sum of squared residuals divided by (T-1), where T is the number of observations.

A test for autocorrelation in the residuals of a linear regression model.

The numerator of the DW statistic, calculated as the sum of squared differences between consecutive residuals.

An approximate function of the estimated autocorrelation coefficient (ρˆ) of the residuals.

The estimated correlation coefficient between the error term at time t and its lagged value at time t-1.

The hypothesis that there is no autocorrelation in the residuals of a linear regression model.

The hypothesis that there is autocorrelation in the residuals of a linear regression model.

The critical values for the DW test that define the rejection regions.

The estimated value of ρˆ based on an estimation of the regression model.

A test that examines the relationship between the error term at time t and multiple lagged values.

The model for the errors under the Breusch-Godfrey test, where the current error term is represented as a linear combination of its lagged values and a random term.

The null hypothesis for the Breusch-Godfrey test, where the current error term is independent of its lagged values.

The alternative hypothesis for the Breusch-Godfrey test, where the current error term is related to at least one of its lagged values.

The conditions that must be met for the DW test to be applicable.

A regression model with a constant term, non-stochastic regressors, and no lags of the dependent variable.