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As explained in this post - > There are low variations in the explanatory variables, low variation of your explanatory variable might affect your results.

The way I used to find that intuitive was graphically : if your values are concentrated on a small range of x then they would less reliable for estimating a slope.

I'm dealing with a continuous variable with low variation (0.3XXXXXXXX to 0.03XXXXXXXX) and I no longer see that explanation intuitive. It seems to me that the scale of X affects the reliability of the predictor. For instance, in an scale of 1.X, this values would be very close together hence affecting the slope, while in a scale of 0.1XXX the reliability of the slope would be different.

So how can I know if my continuous x variable have enough variation for providing a reliable effect on y?

Thank you all in advance for your help.

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  • $\begingroup$ I agree. Good question. $\endgroup$ Apr 26, 2017 at 14:54
  • $\begingroup$ What is a reliable effect? Small variation does not affect estimation within the range of x very much but it would increase the uncertainty for extrapolation. $\endgroup$ Apr 26, 2017 at 15:01
  • $\begingroup$ The best way to assess a scatterplot when you are contemplating a regression is to standardize both variables so that each has the same standard deviation. Otherwise, "low variation" is meaningless. $\endgroup$
    – whuber
    Dec 29, 2023 at 15:38

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First, your variable varies from 0.03 to 0.3. That's a factor of 10! Is that low variation? The fact that the difference is 0.27 is not really relevant. If you want that to be bigger, you could just multiply all the values by 100. This doesn't affect the meaning of the regression. It doesn't matter if you measure height in meters or centimeters.

Second, you need to look at context. Does the variation in your sample match the whole population, at least roughly? If not, this could be restriction of range. For instance, if you are interested in the relationship between high school GPA and college GPA, and you only look at students at Harvard, that will be a problem. Pretty much all the kids at Harvard did really, really well in HS.

So, how do you know? You have to look at the situation and think about it. As so often in real data analysis (and contrary to the image of it) there isn't one simple algorithm that lets you figure this out. Or, as David Cox put it:

There are no routine statistical questions, only questionable statistical routines.

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