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I have a data set which looks as following:

    Y
1   2
1   1.5
1   2.5
2   5
2   3
3   5.2
3   6
3   6.8
4   6
4   7

And the corresponding plot is:

enter image description here

What kind of regression is appropriate for the above kind of data ?

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  • $\begingroup$ I think OLS should work fine on this. Effectively it will try to fit a line through the "midpoints" of the cluster of y values having the same x value, with a bigger weight for the bigger clusters. Presumably that is what you want. $\endgroup$ – noob2 Apr 26 '20 at 12:58
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As noob2 suggested, you run a simple OLS regression (in Excel). You get the estimation result $$\hat{y}_i=0.63+1.61x_i$$ with an $R^2=0.84$. That seems to do the job!

You may want to read this about aggregating the $y_i$ values for the same $x_i$ observation.

enter image description here

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