Acorbic acid content for two cabbage varieties on three planting days. 

cab <- read.table("http://www.rohan.sdsu.edu/~babailey/stat700/cabbage.dat", header=T)

attach(cab)

pdf("cabbage.pdf")
par(mfrow=c(2,2))
stripchart(acid~date,vertical=T, xlab="date", ylab="acid")
stripchart(acid~line,vertical=T, xlab="line", ylab="acid")
interaction.plot(date,line,acid)
interaction.plot(line,date,acid)
mtext("Cabbage Experimental Data", line=-2, outer=T, cex=1)
dev.off()

fit1 <- lm(acid~as.factor(date)*as.factor(line), cab)

> summary(fit1)

Call:
lm(formula = acid ~ as.factor(date) * as.factor(line), data = cab)

Residuals:
    Min      1Q  Median      3Q     Max
-11.900  -5.000  -0.550   4.125  15.600

Coefficients:
                                    Estimate Std. Error t value Pr(>|t|)
(Intercept)                           50.300      2.148  23.419  < 2e-16 ***
as.factor(date)20                     -0.900      3.038  -0.296 0.768139
as.factor(date)21                      4.500      3.038   1.481 0.144288
as.factor(line)52                     12.200      3.038   4.016 0.000184 ***
as.factor(date)20:as.factor(line)52   -2.700      4.296  -0.629 0.532298
as.factor(date)21:as.factor(line)52    4.800      4.296   1.117 0.268766
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 6.792 on 54 degrees of freedom
Multiple R-Squared: 0.5876,     Adjusted R-squared: 0.5494
F-statistic: 15.39 on 5 and 54 DF,  p-value: 2.166e-09

> anova(fit1)
Analysis of Variance Table

Response: acid
                                Df  Sum Sq Mean Sq F value    Pr(>F)
as.factor(date)                  2  909.30  454.65  9.8555 0.0002245 ***
as.factor(line)                  1 2496.15 2496.15 54.1095 1.089e-09 ***
as.factor(date):as.factor(line)  2  144.30   72.15  1.5640 0.2186275
Residuals                       54 2491.10   46.13
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#What about one-way ANOVA and no interaction? 

fit2 <- lm(acid~as.factor(date), cab)
fit3 <- lm(acid~as.factor(line), cab)

> anova(fit2)
Analysis of Variance Table

Response: acid
                Df Sum Sq Mean Sq F value   Pr(>F)
as.factor(date)  2  909.3   454.6  5.0501 0.009567 **
Residuals       57 5131.6    90.0
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

> anova(fit3)
Analysis of Variance Table

Response: acid
                Df Sum Sq Mean Sq F value    Pr(>F)
as.factor(line)  1 2496.2  2496.2  40.843 3.065e-08 ***
Residuals       58 3544.7    61.1
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


fit4 <- lm(acid~as.factor(date) + as.factor(line), cab)

> anova(fit4)
Analysis of Variance Table

Response: acid
                Df  Sum Sq Mean Sq F value    Pr(>F)
as.factor(date)  2  909.30  454.65  9.6609 0.0002486 ***
as.factor(line)  1 2496.15 2496.15 53.0411 1.179e-09 ***
Residuals       56 2635.40   47.06
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#This is regression (and wrong!)

> fit5 <- lm(acid~date, cab)
> fit6 <- lm(acid~line, cab)
> fit7 <- lm(acid~date + line, cab)
>
> anova(fit5)
Analysis of Variance Table

Response: acid
          Df Sum Sq Mean Sq F value Pr(>F)
date       1  190.6   190.6  1.8894 0.1746
Residuals 58 5850.3   100.9
> anova(fit6)
Analysis of Variance Table

Response: acid
          Df Sum Sq Mean Sq F value    Pr(>F)
line       1 2496.2  2496.2  40.843 3.065e-08 ***
Residuals 58 3544.7    61.1
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> anova(fit7)
Analysis of Variance Table

Response: acid
          Df Sum Sq Mean Sq F value    Pr(>F)
date       1  190.6   190.6  3.2386   0.07721 .
line       1 2496.2  2496.2 42.4196 2.052e-08 ***
Residuals 57 3354.1    58.8
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1