An ANOVA can be described as a [regression with dummy variables][1]. You could for example calculate the sums of squares treatment in an ANOVA table using the coefficients from a linear model

    > y <- rnorm(10)
    > x1 <- as.factor(c(0,0,0,0,0,0,1,1,1,1))
    > y.bar <- mean(y)
    > f1 <- lm(y ~ x1)
    > sum(((f1$coef[1]) - y.bar)^2)*6 + sum(((f1$coef[1] + f1$coef[2]) - y.bar)^2)*4
    [1] 1.784887
    > anova(f1)
    Analysis of Variance Table
    
    Response: y
              Df Sum Sq Mean Sq F value Pr(>F)
    x1         1 1.7849  1.7849   1.596  0.242
    Residuals  8 8.9470  1.1184

                  
However, when using two or more continuous predictors 

    > x2 <- rnorm(10)
    > x3 <- rnorm(10)
    > f2 <- lm(y ~ x2 + x3)
    > anova(f2)
    Analysis of Variance Table
    
    Response: y
              Df Sum Sq Mean Sq F value Pr(>F)
    x2         1 0.7797 0.77970  0.5959 0.4654
    x3         1 0.7934 0.79336  0.6064 0.4617
    Residuals  7 9.1588 1.30841


How are sums of squares calculated and how could they be interpreted?

  


  [1]: https://stats.stackexchange.com/questions/175246/why-is-anova-equivalent-to-linear-regression