for each of these there is a set of assumptions that must be met in order for the test results to be valid
Simple Linear Model:
(1) Linearity
(2) Independence of Errors
(3) Homoskedasticity
(4) Normality of Errors
ANOVA Test:
(1) Normality
(2) Homogeneity of Variance
(3) Independence
I hope that helps! If you're interested in learning more about what each of those entails, feel free to shoot me a message!