# Residuals Calculator (with Examples)

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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.

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