0
$\begingroup$

Below i have attached a scatter plot showing my dependent variable on the Y-axis and my independent variable on the X-axis

I am not sure if the linearity assumption is violated? Can anyone explain if this is the case, or if the assumption is satisfied?

All the best

enter image description here

Improve this question
$\endgroup$
3
  • $\begingroup$ It appears that the linearity assumption is just fine -- there's just no slope. In other words, it appears by eyeballing this that the conditional distribution of $y$ (your dependent variable) given $x$ (your independent variable) is no different from the marginal distribution of $y$. In other words, it seems the average value is 2 is a good prediction, regardless of the level of your independent variable. To be clear, there's no obvious trend, but an analysis can easily verify this. There may be some dip in your mean response for values around 50-150 of your dependent var. though. $\endgroup$
    – StatsStudent
    Commented Apr 26, 2019 at 15:19
  • $\begingroup$ Hi. Thanks a lot. What analysis could verify this? $\endgroup$
    – maS
    Commented Apr 26, 2019 at 17:24
  • $\begingroup$ You might want to fit a spline to the data. You may also carry out a the F test for lack of fit since it appears you have multiple observations at the same at one or more levels of your dependent variable. See Section 3.7 (page 119) of Applied Linear Statistical Models, 5th, by Kutner, et. al. $\endgroup$
    – StatsStudent
    Commented Apr 26, 2019 at 19:37

1 Answer 1

Reset to default
1
$\begingroup$

There are no obvious nonlinearities between your dependent and independent variables, like a parabolic or exponential curve, so my humble opinion is that you are fine as far as the linearity assumption goes. Just looking at your plot, I would be more concerned about whether there is even a linear relationship between your two variables, though there could certainly be something there that is not visible to the naked eye.

If you don't find a linear relationship, it wouldn't hurt to transform either your dependent variable or your independent variable and see if there is a statistically significant nonlinear relationship (you could try $\log X$ or $X^2$). But if you do find a linear relationship that fits with what is already known in your field, I wouldn't worry too much about the linearity assumption based on this plot.

If does seem like the number of values taken by the response is limited. Perhaps your response is already transformed from count data? Wouldn't really change anything, except you probably wouldn't want to transform it more than once, as that would make interpretation more difficult.

Improve this answer
$\endgroup$
2
  • $\begingroup$ Hi. Thanks a lot for youre answer. My dependent variable is already log transformed. Do you think it would make more sense, to make the independent variable a categorial instead of a continuous? The independent variable expresses cultural distance so i guess i could group it into low distance, medium distance and high distance?.. Or can i just assume that the linearity assumption holds? $\endgroup$
    – maS
    Commented Apr 26, 2019 at 17:27
  • $\begingroup$ I wouldn't make your response categorical unless it somehow made interpretation easier, especially since I think it wouldn't help you at all regarding the linearity assumption. I personally feel that you are fine assuming a linear relationship, especially if there is no previous work done by others suggesting a nonlinear relationship. $\endgroup$
    – dante
    Commented Apr 26, 2019 at 19:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.