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To conduct a MLR it is required that each variable has a linear relationship to the DV. However, in my current study, the variables have a weak relationship with the DV. This makes it quite hard to tell if the linearity assumption has been met from the scatterplot.

It is also worth noting that this is a replication study, and all variables have previously been shown to have a significant linear relationship to the DV (so they are informed by theory).

Given this situation, is it still possible to use these variables to form a model in MLR? If not, what alternatives do i have?

**Scatterplots for reference **

Variable 1.

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Variable 2.

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Variable 3.

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Andrew Drewmore
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2 Answers2

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Yes. Selecting DVs for your model depends on what question you are trying to answer and what behavior you expect from the variables based on subject matter knowledge. For example, you might be interested in the relationship between variable X1 and Y, whilst controling for variable X2. Often you need to include such a variable even if it not significant, becasue you are expected to do so in your research area (e.g. age and sex in medical research). Also, it can occur that variables X1 and X2 are not related to Y in univariate anlayses, but are both related to Y when entered to the model at the same time. You may also use categorical variables as dependent variables in multiple linear regression, which will not be linearly related to Y. Regression models should be constructed primarily based on subject matter knowldge to get the most meaningful answers.

Uki Buki
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  • This makes more sense now. Thank you for answering. For some context, in this study, I'm trying to use 3 variables to predict a DV to replicate the previous findings. So, therefore, I can say that even though the scatterplots don't show a linear relationship, they will be kept in the model due to current subject matter knowledge (i.e. previous research). – Andrew Drewmore Jul 19 '22 at 14:03
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Is possible to use, because the model can capture some linear trend in data. Some alternatives for your study:

  • Use regularization in order to penalize weak relationships
  • Use generalized additive models in order to taking account the non linearity
  • Transform the variables before hand in order to making the relationship more linear, I not sure if it would be 100% rigorous or double dipping.

BTW look at this: Can a linear regression be significant if the data is not linear?

Allan
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