Regression Model:
A regression model is a statistical approach used to predict the relationship between a dependent variable and one or more independent variables. It is a mathematical representation of the functional relationship between the variables under consideration. The regression model helps in understanding and analyzing the impact of independent variables on the dependent variable.

Estimated Regression Equation:
The estimated regression equation is the equation that represents the relationship between the dependent variable and the independent variable(s) based on the data. It is derived from the regression model using statistical techniques such as least squares estimation. The estimated regression equation is used to estimate the values of the dependent variable for given values of the independent variable(s).

Differences between Regression Model and Estimated Regression Equation:

1. Concept:
- The regression model is a conceptual framework that explains the relationship between the dependent and independent variables.
- The estimated regression equation is a specific equation derived from the regression model using data.

2. Purpose:
- The regression model is used to understand and analyze the relationship between variables, identify significant predictors, and make predictions.
- The estimated regression equation is used to estimate the values of the dependent variable based on the given independent variable(s).

3. Representation:
- The regression model is represented by an equation that includes both the dependent and independent variables along with the coefficients.
- The estimated regression equation is derived from the regression model and includes only the estimated coefficients.

4. Applicability:
- The regression model is applicable to a population or a specified population segment.
- The estimated regression equation is applicable to the observed data used to estimate the coefficients.

5. Statistical Techniques:
- The regression model is developed using statistical techniques such as model selection, hypothesis testing, and goodness-of-fit measures.
- The estimated regression equation is derived using techniques like least squares estimation to minimize the sum of squared residuals.

6. Generalization:
- The regression model allows for generalization to the population from which the sample is drawn.
- The estimated regression equation provides specific estimates for the observed data used to estimate the coefficients.

In summary, the regression model is a conceptual framework that explains the relationship between variables, while the estimated regression equation is a specific equation derived from the model using statistical techniques. The model provides a broader understanding, while the equation provides specific estimates for observed data.