Linear and Non-Linear Regression

In summary, the individual has conducted a regression analysis and plotted a graph of their residuals vs their input variable. They are aware that for a linear regression, the residuals must be randomly scattered, but the graph appears to have a curve. They are wondering if this is due to the small number of data points or if the relationship is not linear. They attempted to use the log of their output and tried cubic and quadratics, resulting in a slightly smaller R squared value. They believe this suggests a non-linear relationship, but are unsure of the next steps to take. They are seeking guidance on what to look for next.
  • #1
Dollydaggerxo
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Homework Statement


Well I have conducted a regression analysis, and have plotted a graph of my residuals vs my input variable. I know that for a linear regression the residuals must be randomly scattered blahblah, but from this graph, it looks like it has a curve to it ? is this because I only have 10 points, or is it not linear?
If it is not linear, where do I go from there?

Homework Equations


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The Attempt at a Solution


Assuming it is not linear, I tried to do the log to the base ten of my output, and ended up with a slightly smaller value of R squared. I also tested with cubic and quadratics, they seem to have a larger value of R squared.
 
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  • #2
I think this implies that the relationship is not linear, but I am still stuck on what to do next. Is there something else i should be looking for?
 

What is linear regression?

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It assumes that there is a linear relationship between the variables and uses this to make predictions.

What is non-linear regression?

Non-linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables when the relationship is not linear. It uses a non-linear function to fit the data and make predictions.

What is the difference between linear and non-linear regression?

The main difference between linear and non-linear regression is the type of relationship between the dependent and independent variables. Linear regression assumes a linear relationship, while non-linear regression allows for a more complex, non-linear relationship.

When is linear regression appropriate to use?

Linear regression is appropriate to use when there is a clear linear relationship between the dependent and independent variables. This can be determined by visually inspecting a scatter plot of the data or by conducting a statistical test.

Can non-linear regression be used for all types of data?

No, non-linear regression may not be appropriate for all types of data. It is best suited for data that shows a non-linear relationship between the variables. If the relationship is linear, then linear regression should be used instead.

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