An Overview of Regression Analysis.

1. Basic ideas of Linear Regression
2. Estimation of Parameters by Ordinary Least Squares (OLS)
3. Coefficient of Determination and Coefficient of Correlation
4. Prediction with the Simple Regression Model

1. Econometrics Modelling
2. Assumptions Underlying OLS
3. The Properties of OLS Estimators
4. Estimation of Parameters
5. Goodness of Fit of Estimated Multiple Regression
6. Hypothesis Testing in Multiple Regression Model

1. Linear model
2. Double log model
3. Semi-log model: Log-linear model / Linear-log model
4. Polynomial model
5. Reciprocal model

1. Nature of dummy variables
2. Slope and Intercept Dummies

1. Specification error
2. Multicollinearity
3. Heteroscedasticity
4. Autocorrelation

A1 : Simple linear regression model contains one dependent variable (DV) and one independent variable (IV). Multiple linear regression model, on the other hand, contains one DV and more than one IVs.

A2 : Ordinary Least Squares (OLS) is a statistical method used in regression analysis to estimate the relationship between a dependent variable and one or more independent variables. OLS minimizes the sum of the squared differences (residuals) between the observed values and the predicted values from a linear model.

A3 : A dummy variable (also known as an indicator variable or binary variable) is a numerical variable used in regression analysis to represent categorical data with two or more categories. Dummy variables allow qualitative characteristics (such as gender, region/location, or type of institution) to be included in a regression model. Often it takes on the values 0 or 1 only, where 0 typically represents the absence of a characteristic (baseline or reference group), and 1 represents the presence of a particular category or characteristic.

Suppose we want to include gender in a regression model, where: Gender=1 is for male, and Gender=0 is for female. Here, female is the reference category.

A4 : In multiple regression analysis, the classical linear regression model (CLRM) relies on several key assumptions to ensure that the Ordinary Least Squares (OLS) estimator is Best Linear Unbiased Estimator (BLUE). Violations of these assumptions lead to econometric problems that compromise the consistency and validity of the regression results. The common problems in multiple regression analysis are such as specification error, multicollinearity, heteroskedasticity, and serial correlation.