Pupil:

What is a residual?

Mentor:

Well, a residue is the difference betwixt the measured value and the predicted value of a regression model. It is important to empathize residuals because they show how accurate a mathematical function, such as a line, is in representing a set of information. To find a residual yous must take the predicted value and subtract it from the measured value.

Educatee:

What are the predicted values? How do you find that?

Mentor:

The line of best fit provides the predicted values for a set of information. For example, with the line of all-time fit the predicted value is the value on the line that corresponds to a specific independent value. Take a await at the graph. The y-coordinate values on the line of all-time fit lucifer the x-values from the data ready.

Now allow’s use the Regression Activity to calculate a residual! First, let’s plot the following four data points: {(ane, 2) (2, 4) (3, 6) (four, 5)}. The labels x and y are used to stand for the independent and dependent variables correspondingly on a graph. These given y-values (dependent variables) are the measured values for the specified ten-values (independent variables). Now, let’s graph the line of all-time fit past selecting

*Display line of best fit*

and see where the predicted values lie on the graph.

Educatee:

Cool! Now I tin come across what y’all mean about the predicted and the observed values!

Mentor:

Great, now allow’southward endeavour to find the residuum for the contained variable, x = 1. How would you do this?

Student:

Well, I would starting time write down the measured value for independent variable x=i, which would be 2 since I plotted (1, two). Now, I run across that when the ten-value is one, the y-value on the line of best fit is approximately two.vi. Then, to find the residuum I would subtract the predicted value from the measured value and so for ten-value 1 the residual would be 2 – 2.6 = -0.six.

Mentor:

That is right! The residuum of the contained variable x=one is -0.6. If yous are having trouble remembering which value to subtract from which you tin can think about information technology this way: yous are trying to run into how far off the predicted value is from the actual value so you lot would want to have the bodily value and subtract the predicted value to run across how far off the predicted value is from the actual value. Sometimes the residual will exist positive and sometimes it will be negative. When practicing finding residuals you can also use the Regression Activity and select

*show residuals*

to compare your findings.

Pupil:

Absurd! Under the column X the value ane corresponds with the number -0.6 under the column

*line of best fit*. The residuum is -0.half-dozen for x=1, then do the numbers in the

*line of all-time fit*

column represent the residuals for each ten-value?

Mentor:

Yep. Also, the Residuum Plot graphs the residuals as the y-values with the corresponding x-values. The Residual Plot gives you lot a visual way of representing residuals of independent and dependent variables.

Student:

This is actually helpful – now I know how to find residuals!

## Which is the Residual Value When X 2

Source: http://www.shodor.org/interactivate/discussions/FindingResiduals/