Enter the observed and expected values into the calculator to determine the residual. The residual is the difference between these two values and is used in regression analysis to identify the deviation of data points from the regression line.
Residual Formula
The following formula is used to calculate the residual:
R = O - E
Variables:
- R is the residual
- O is the observed value
- E is the expected value
To calculate the residual, subtract the expected value from the observed value.
What is a Residual?
A residual is a measure used in statistical analyses, particularly in regression analysis, to determine the difference between observed and predicted values of a dependent variable. The residual for each data point is the vertical distance between the point and the regression line; it is positive if the point is above the line and negative if below. Residuals are crucial for diagnosing the fit of a regression model and for identifying outliers or non-linear patterns.
How to Calculate a Residual?
The following steps outline how to calculate the residual:
- First, determine the observed value (O).
- Next, determine the expected value (E).
- Use the formula R = O – E to calculate the residual (R).
- Finally, compare the residual to assess the accuracy of the prediction.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
Observed value (O) = 50
Expected value (E) = 45