Meaning of Homoscedasticity I'm doing a simple linear regression project (only one feature), and I am checking the assumptions, however, I don't really understand the reasoning behind our homoscedasticity assumption. I've looked all over for a solution, but all of the answers are hard for me to understand. Could someone please explain to me why the residuals need to have constant variance in layman's terms. Thank you in advance if anyone can help me.

Without doing any math, when we calculate p-values and confidence intervals, we are calculating them based on wrong distributions. If we assume constant variance, those p-values and confidence intervals are calculated a certain way to give the properties that we expect them to have, and without constant variance, those properties will not hold.
Consequently, while a (say) $95\%$ confidence intervals is supposed to contain the true value $95\%$ of the time, we might wind up in a position where such a confidence interval contains the true value $90\%$ of the time, maybe $80\%$ or $60\%$ of the time. However it happens, we wind up being more confident than we should be, since what we think is a $95\%$ confidence interval is really a $90\%$ (or $80\%$ or $60\%$) confidence interval.
