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I am performing an univariate linear regression analysis. Before running the model I was always told to get an idea of the relationship between the independent and dependent variable through a scatterplot and look for a pattern.

I always do that but without understand the real consequences on my regression analysis.

What I would like to ask you is to "friendly" explain the purpose of making a scatterplot for the relationship between dependent and independent variable and, more importantly, how my analysis would change if I have a linear, logarithmic, exponential, quadratic, cubic or square root relationship coming out from my scatterplot.

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A scatterplot is not only useful to detect potential non-linear relationships but also outliers/extreme values and possible heteroscedasticity (non-homogeneous variance) both of which may influence the regression results. In cases of a non-linear (e.g., u-shaped) relationship, we would consider modeling this relationship appropriately, for example, by adding a quadratic term to the regression model. Otherwise, the regression model would be misspecified and may lead to incorrect conclusions.

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  • $\begingroup$ What about a logarithmic-shaped relationship? What the theory or the standard practice would suggest to do in this case? $\endgroup$
    – fredi96
    Sep 20, 2023 at 10:48

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