# ANOVA test p-value interpretation

model = lm(Sepal.Width ~ Sepal.Length + Petal.Length, data = iris)
> summary(model)

Call:
lm(formula = Sepal.Width ~ Sepal.Length + Petal.Length, data = iris)

Residuals:
Min       1Q   Median       3Q      Max
-0.86412 -0.21142  0.00315  0.20406  0.73806

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)   1.03807    0.28817   3.602 0.000431 ***
Sepal.Length  0.56119    0.06533   8.590 1.16e-14 ***
Petal.Length -0.33527    0.03065 -10.940  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.3235 on 147 degrees of freedom
Multiple R-squared:  0.4564,    Adjusted R-squared:  0.449
F-statistic: 61.71 on 2 and 147 DF,  p-value: < 2.2e-16


I have a regression model $Y_i = \beta_0 + \beta_1 * SepalLength_i + \beta_2 * PetalLength_i + \epsilon_i$. Looking at the Pr(>|t|) column, I know that these are the p-values of a t-test for the significance of a corresponding $\beta_i$. For instance, the p value 1.16e-14 corresponds to a t-test for $H_0: \beta_1 = 0$ v.s $H_1: \beta_1 \neq 0$. As for the p-value associated with the F statistic (p-value: < 2.2e-16) that corresponds to the test of $H_0: \beta_1 = \beta_2 = 0$ v.s $H_1:$ at least one of $\beta_1 or \beta_2 \neq 0$.

> anova(model)
Analysis of Variance Table

Response: Sepal.Width
Df  Sum Sq Mean Sq F value  Pr(>F)
Sepal.Length   1  0.3913  0.3913   3.738 0.05511 .
Petal.Length   1 12.5284 12.5284 119.689 < 2e-16 ***
Residuals    147 15.3872  0.1047
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Looking at the ANOVA table, how do I interpret the last column with the p-values? What hypotheses am I testing here?