CORE help?

[Ceres]

Hello! I'm currently doing my Further SAC revision and I don't understand Residual plots.
How can I tell if a data will be linear or not from it? Also, how can I tell the strength of the linearity?
My textbook tells me that when there's no clear pattern, that means the data is linear. However, in my recent maths test I got a question wrong with the correct answer being:
 'There is no clear pattern in this residual plot, therefore it can be concluded that the linear relationship between the two variable is weak.'

Sorry, I'm quite bad at Mathematics :[

[Stick]

Hello! I'm currently doing my Further SAC revision and I don't understand Residual plots.
How can I tell if a data will be linear or not from it? Also, how can I tell the strength of the linearity?
My textbook tells me that when there's no clear pattern, that means the data is linear. However, in my recent maths test I got a question wrong with the correct answer being:
 'There is no clear pattern in this residual plot, therefore it can be concluded that the linear relationship between the two variable is weak.'

Sorry, I'm quite bad at Mathematics :[

Don't worry, hopefully you'll be able to understand these concepts now that I explain them to you.

Basically, a residual plot is the best way to test for linearity. However, you shouldn't use this technique on its own to determine the strength of a linear relationship. You should use Pearson's correlation co-efficient (r) and the co-efficient of determination (r^2) in conjunction with a residual plot to not only verify whether a relationship is linear, but how linear it is. One could judge how close the residual points are relative to the x-axis and assume that if they're very close that the linear relationship is strong, but this not reliable, especially if we're dealing with very small data values. 'Turning your head' and using the normal graph as a residual plot (in terms of determining linearity, not residual values) is the only shortcut I can think of, but that too is a bit cumbersome.

In regards to the answer that you provided, I'm a bit flummoxed. Your textbook definition is correct, and the answer provided really isn't. Bring this up with your teacher immediately.

[Ceres]

Don't worry, hopefully you'll be able to understand these concepts now that I explain them to you.

Basically, a residual plot is the best way to test for linearity. However, you shouldn't use this technique on its own to determine the strength of a linear relationship. You should use Pearson's correlation co-efficient (r) and the co-efficient of determination (r^2) in conjunction with a residual plot to not only verify whether a relationship is linear, but how linear it is. One could judge how close the residual points are relative to the x-axis and assume that if they're very close that the linear relationship is strong, but this not reliable, especially if we're dealing with very small data values. 'Turning your head' and using the normal graph as a residual plot (in terms of determining linearity, not residual values) is the only shortcut I can think of, but that too is a bit cumbersome.

In regards to the answer that you provided, I'm a bit flummoxed. Your textbook definition is correct, and the answer provided really isn't. Bring this up with your teacher immediately.

Thank you so much for helping and the quick reply!

Quick question, can I bump this thread if I need more help, or do I need to make a new thread?
(New to the forums)

[Yacoubb]

However, in my recent maths test I got a question wrong with the correct answer being:
 'There is no clear pattern in this residual plot, therefore it can be concluded that the linear relationship between the two variable is weak.'

That isn't a good explanation. IF the residual plot shows a clear pattern, this indicates that there is a non-linear pattern and that a linear model (e.g. regression model) is not appropariate to describe the relationship between the IV and the DV.

If the plots of a residual plot are randomly scattered and show no clear pattern, this indicates that the relationship between the IV and DV is linear, and that therefore, a linear model can be used to describe the relationship between the IV and the DV.

It's not a really good explanation because you can still have a strong negative or positive relationship with a non-linear relationship; and remember. Pearson's Correlation Coefficient (r) gives the indication of the strength of the relationship between the dependent and independent variable.

The Coefficient of determination (r²) can still also be a relatively high percentage with a non-linear relationship; hence, as Stick was mentioning, why you must look at several different factors + direct observation of your scatterplot of course in determining whether the relationship is linear/non-linear.

[Ceres]

That isn't a good explanation. IF the residual plot shows a clear pattern, this indicates that there is a non-linear pattern and that a linear model (e.g. regression model) is not appropariate to describe the relationship between the IV and the DV.

If the plots of a residual plot are randomly scattered and show no clear pattern, this indicates that the relationship between the IV and DV is linear, and that therefore, a linear model can be used to describe the relationship between the IV and the DV.

It's not a really good explanation because you can still have a strong negative or positive relationship with a non-linear relationship; and remember. Pearson's Correlation Coefficient (r) gives the indication of the strength of the relationship between the dependent and independent variable.

The Coefficient of determination (r²) can still also be a relatively high percentage with a non-linear relationship; hence, as Stick was mentioning, why you must look at several different factors + direct observation of your scatterplot of course in determining whether the relationship is linear/non-linear.

Thanks for the reply!