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Non-linear regression & residuals
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The sum of square residuals SSres and the coefficient of determination R2. Using the calculator to fit linear, quadratic, cubic, exponential, power or sine models.
Want a deeper conceptual understanding? Try our interactive lesson!
Sum of square Residuals
AHL AI 4.13
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:
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.
The coefficient of determination R²
AHL AI 4.13
The coefficient of determination, denoted R2, is the most commonly used measure for how well a model fits the data.
In plain terms, R2 answers the question "What fraction of the spread in the data is explained by the model?".
It takes values between 0 and 1, which you can think of as between
0% of the variation is explained by the model, which means the model is completely useless.
100% of the variation is explained by the model, which means the model perfectly predicts the values observed.
Note that an R2 value of 1 does not mean that the model will perfectly predict other values.
Quadratic, cubic, exponential and power regression
AHL AI 4.13
The IB expects you to know how to use given data and your calculator to fit models of the following types:
You will also need to use sin regression, but it works a little differently so we'll explain it right after this.
All of the models in the table work the same on your calculator:
Enter the x list (usually into L1)
Enter the y list (usually into L2)
Navigate to stat>calc and scroll down to find the right model.
Select the XList and YList you entered.
Scroll down to calculate, hit enter, and the calculator returns the parameters (a,b etc) and the value of R2.
Sinusoidal regression with technology
AHL AI 4.13
Your calculator should have a function called sinusoidal regression which you can use when you know at least 4 points on a sinusoidal function, and you can estimate the period. To use it, first enter the x coordinates (or independent variables) into L1 and the y coordinates (or dependent variable) into L2.
The calculator will likely ask you to provide a number for "iterations", which is simply the number of "loops" it makes in refining its approximation. 5 will be plenty unless a problem asks for a very high degree of accuracy.
Nice work completing Non-linear regression & residuals, here's a quick recap of what we covered:
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