<p>This has to do with whether a question has an accepted answer, and/or whether your answer was accepted.  </p>

<p>When you look at a list of questions, the icon is filled green if that question has an accepted answer.  Consider these three from the list generated by the <a href="https://stats.stackexchange.com/questions/tagged/regression" class="post-tag" title="show questions tagged &#39;regression&#39;" rel="tag">regression</a> tag:  </p>

<p><a href="https://i.stack.imgur.com/jUbxJ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/jUbxJ.png" alt="enter image description here"></a></p>

<p>The first thread, <a href="https://stats.stackexchange.com/questions/231142/linear-regression-with-partially-known-coefficients">linear regression with partially known coefficients</a>, has one answer, which has been accepted.  The last thread, <a href="https://stats.stackexchange.com/questions/231117/how-to-calculate-bias-when-we-have-an-estimation-using-simple-linear-regression">How to calculate bias when we have an estimation using simple linear regression?</a>, has one answer, which has not (yet?) been accepted.  </p>

<p>When you look at your reputation page, you will see a filled green icon representing the reputation you gained from having one of your answers accepted.  Here is a section of your reputation page:  </p>

<p><a href="https://i.stack.imgur.com/pDsFK.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/pDsFK.png" alt="enter image description here"></a></p>

<p>When the reputation gains from August 14th are expanded, you can see that the icon is filled green because you received 15 points from when your answer to <a href="https://stats.stackexchange.com/questions/222084/is-there-such-a-thing-as-an-adjusted-r2-for-a-quantile-regression-model">Is there such a thing as an adjusted $R^2$ for a quantile regression model?</a> was accepted (congratulations).  Note that the reputation you gained from the upvote is not filled green.  </p>

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<p>Regarding the screenshot of your homepage, <em>On round robin</em> is green under questions because it is a question with an accepted answer. The square isn't green under reputation because you didn't earn that 5 points of reputation by having an answer accepted (but by having your question upoted).  </p>
