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Perplex
  • Dashboard
Topics
Exponents & LogarithmsRounding & ErrorSequences & SeriesFinancial MathematicsMatricesComplex Numbers
Cartesian plane & linesFunction TheoryModellingTransformations & asymptotes
2D & 3D GeometryVoronoi DiagramsTrig equations & identitiesVectorsGraph Theory
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DifferentiationIntegrationDifferential Equations
Paper 3
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Perplex

Bivariate Statistics (Lesson 3/3)

Non-linear regression & residuals

1 / 6

Sum of square Residuals

The sum of square residuals, denoted ​SSres​, is a measure of fit for a model. It works like this:

  • Take the difference between the actual values ​yi​​ and the values predicted by the model, which we call ​y^​i​.

  • Square each of those differences

  • Add them all up to find ​SSres​​

In short, ​SSres​​ is how far off the model is at each point, squared, and added for all the points. Visually, ​SSres​​ is the sum of the areas of these squares:

In IB exams, you need to know how to find it from a table:

​yi​​

​1​

​2​

​3​

​y^​i​​

​0.9​

​1.5​

​3.2​

​ri2​​

​(1−0.9)2=0.01​

​0.25​

​0.04​

Adding these all up gives

​
SSres​=0.01+0.25+0.04=0.3
​

You can use your calculator to do this more quickly using list and summation features.

Bivariate Statistics (Lesson 3/3)

Non-linear regression & residuals

1 / 6

Sum of square Residuals

The sum of square residuals, denoted ​SSres​, is a measure of fit for a model. It works like this:

  • Take the difference between the actual values ​yi​​ and the values predicted by the model, which we call ​y^​i​.

  • Square each of those differences

  • Add them all up to find ​SSres​​

In short, ​SSres​​ is how far off the model is at each point, squared, and added for all the points. Visually, ​SSres​​ is the sum of the areas of these squares:

In IB exams, you need to know how to find it from a table:

​yi​​

​1​

​2​

​3​

​y^​i​​

​0.9​

​1.5​

​3.2​

​ri2​​

​(1−0.9)2=0.01​

​0.25​

​0.04​

Adding these all up gives

​
SSres​=0.01+0.25+0.04=0.3
​

You can use your calculator to do this more quickly using list and summation features.