> x.hours <- 2*hours+4          
> piece.aov <- aov(y~factor(hours))
> summary(piece.aov)
              Df  Sum Sq Mean Sq F value    Pr(>F)    
factor(hours)  3 1808.68  602.89  141.46 2.173e-15 ***
Residuals     24  102.29    4.26                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> TukeyHSD(piece.aov,'factor(hours)')
  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = y ~ factor(hours))

$`factor(hours)`
         diff       lwr       upr     p adj
2-1  9.857143  6.813050 12.901236 0.0000000
3-1 16.571429 13.527335 19.615522 0.0000000
4-1 21.428571 18.384478 24.472665 0.0000000
3-2  6.714286  3.670192  9.758379 0.0000157
4-2 11.571429  8.527335 14.615522 0.0000000
4-3  4.857143  1.813050  7.901236 0.0010237

> 
> piece.quad <- lm(y ~ x.hours + I(x.hours^2))
> summary(piece.quad)

Call:
lm(formula = y ~ x.hours + I(x.hours^2))

Residuals:
    Min      1Q  Median      3Q     Max 
-4.0643 -1.0643  0.3357  1.2607  3.3357 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -3.73571    7.45494  -0.501   0.6207    
x.hours       9.17500    1.73352   5.293 1.75e-05 ***
I(x.hours^2) -0.31250    0.09583  -3.261   0.0032 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 2.028 on 25 degrees of freedom
Multiple R-squared: 0.9462,     Adjusted R-squared: 0.9419 
F-statistic: 219.7 on 2 and 25 DF,  p-value: < 2.2e-16 

> anova(piece.quad)
Analysis of Variance Table

Response: y
             Df  Sum Sq Mean Sq F value Pr(>F)    
x.hours       1 1764.35 1764.35 428.805 <2e-16 ***
I(x.hours^2)  1   43.75   43.75  10.633 0.0032 ** 
Residuals    25  102.86    4.11                   
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> 
> anova(piece.quad,piece.aov)
Analysis of Variance Table

Model 1: y ~ x.hours + I(x.hours^2)
Model 2: y ~ factor(hours)
  Res.Df    RSS Df Sum of Sq      F Pr(>F)
1     25 102.86                           
2     24 102.29  1   0.57857 0.1358 0.7158
> 
> plot(x.hours,y,xlab="Hours of Training",ylab="Number of Acceptable Units")
> 
> xs <- seq(6,12,.1)
> 
> lines(xs,coef(piece.quad)[1]+coef(piece.quad)[2]*xs+coef(piece.quad)[3]*xs^2)
>