The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is known as the "residual" or "error".

Here are the steps to understand this:

1. In a regression analysis, we have a dependent variable (also known as the outcome or response variable) and one or more independent variables (also known as predictors or explanatory variables).

2. We use the independent variables to predict the dependent variable. This prediction is based on the estimated regression equation, which is derived from the data.

3. However, this prediction is not always perfect. There is usually some difference between the actual observed value of the dependent variable and the value predicted by the regression equation.

4. This difference is called the "residual" or "error". It represents the amount of variation in the dependent variable that is not explained by the independent variables.

5. The goal of regression analysis is to minimize these residuals, i.e., to make the predictions as close as possible to the observed values.