In chapter 4.1 Simple Linear Regression we have to look at how to find a linear equation that explains the data. In this chapter, we will look at other forms of equations. The rationale is to try more regression lines and use the one with the higher value of R squared (obviously, if you find at least one with a good R squared).



Exponential

The exponential equation has a form expressed in the image1.

Image1 – Exponential equation

In this case the scatter plot with the regression line appear like the one in image2.

Image2 - Scatter plot with exponential regression line
Image2 – Scatter plot with exponential regression line

In this case, we have an R squared very high to say that the exponential regression explains the data.


Logarithmic

The logarithmic equation has a form expressed in the image3.

Image3 - Logarithmic equation
Image3 – Logarithmic equation

In this case, the scatter plot with the regression line appears like the one in the image4.

Image4 -  Scatter plot with logarithmic regression line
Image4 – Scatter plot with logarithmic regression line

In this case, we have an R squared not so high, so for now the exponential regression line is better.


Power

The power equation has a form expressed in the image5.

Image5 - Power equation
Image5 – Power equation

In this case, the scatter plot with the regression line appears like the one in the image6.

Image6 -  Scatter plot with power regression line
Image6 – Scatter plot with power regression line

In this case, we have an R squared very very high, so this is better than exponential.


All these graphs are made by excel scatter plot and then, clicking on one data point, adding the regression line, the equation, and the R Squared.

For the exam remember that:

  • You can use single non-linear regression when your observation isn’t linear;
  • Some examples of non-linear regression is Exponential, Logarithmic, and Power;
  • They work like the single linear regression but with a different shape of the equation.
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