The residuals calculator below will find the residual values on the basis of the values for the independent (X variable) and dependent (Y variable) variables entered.

We construct a linear regression model to predict the values of the dependent variable. But it is not necessary that the dependent variable takes the values that the model predicts.

**The residuals are the difference between the predicted and the actual values of the dependent variable.** Hence the residuals measure the error in our model.

Enter the data values in the calculator below to obtain the required residual values.

**Linear Regression Equation:**

ŷ = 7.8900 + (1.3411)*x

**List of Residuals:**

-1.572

0.428

-0.255

-2.619

0.040

-6.348

0.311

10.016

**Example:**

Suppose that we apply the method of linear regression the following set of data values:

**X Values: 2, 2, 4, 8, 9, 16, 17, 12**

**Y Values: 9, 11, 13, 16, 20, 23, 31, 34**

We can check using the above calculator that the regression equation for the above data values turns out to be,

**ŷ = 7.8900 + (1.3411)*x**

Let us obtain the residual for the first data pair X = 2, Y = 9.

The predicted value for Y can be found by substituting x = 2 in the regression equation.

**Predicted Value = ŷ = 7.8900 + (1.3411)*2 = 7.8900 + 2.6822 = 10.5722**

But, the actual Y value for X = 2 is,

** Actual value (Y) = 9**

**Residual = Actual Value – Predicted Value = 9 – 10.5722 = -1.572**

We can similarly calculate the residual for the remaining seven values.