Difference between Observed Value and Estimated Value in Regression Analysis

Introduction:
Regression analysis is a statistical technique used to analyze the relationship between two or more variables. It is used to predict the value of one variable based on the value of another variable. The goal of regression analysis is to find the best fit line that can explain the relationship between the variables. The difference between the observed value and estimated value is known as the error, residue, or deviation.

Error:
The error is the difference between the observed value and the predicted value. It is also known as the residual. The error is the measure of the accuracy of the regression model. A good regression model should have a small error value. The error can be positive or negative. A positive error means that the observed value is greater than the predicted value, and a negative error means that the observed value is less than the predicted value.

Residue:
Residue is another term used for the difference between the observed value and the estimated value. In regression analysis, residue is often used to refer to the difference between the observed value and the fitted value. The fitted value is the value predicted by the regression model. The residue can be positive or negative, depending on whether the observed value is greater or less than the fitted value.

Deviation:
Deviation is also used to refer to the difference between the observed value and the estimated value. Deviation is a measure of how much the data points deviate from the regression line. The deviation can be positive or negative. A positive deviation means that the data point is above the regression line, and a negative deviation means that the data point is below the regression line.

Conclusion:
In conclusion, the difference between the observed value and estimated value in regression analysis can be referred to as the error, residue, or deviation. These terms are used interchangeably to describe the same concept. The error, residue, or deviation is a measure of the accuracy of the regression model. A good regression model should have a small error value, and the data points should be close to the regression line.