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.


why the residuals need to have constant variance in layman's terms

The assumption of homogeneity of variance is important for inference on the coefficients of the model (which are interpreted as the average effects of the variable on the outcome).
The sampling variance of the coefficient $\beta_1$ (the slope) in a linear regression involves the estimated variance
$$ \mathrm{Var}\left(\hat{\beta}_1\right)=\sigma^2 /\left[\mathrm{SST}_1\left(1-R_1^2\right)\right]$$
If $\sigma^2$ is not constant (e.g. is a function of the predictor), then the variance is misspecified and hence the standard error (and consequently confidence intervals and p values) will also be incorrect.
When homogeneity of variance is violated, there exist methods for correcting the standard errors.  See "robust standard errors" or "the sandwich estimator"
