> gasblend.mod1 <- aov(y ~ x1 + x2 + x3 + I(x1*x2) + I(x1*x3) + I(x2*x3) + trt)
> anova(gasblend.mod1)
Analysis of Variance Table

Response: y
           Df Sum Sq Mean Sq F value    Pr(>F)    
x1          1 443.90  443.90 42.1418 0.0003368 ***
x2          1 221.78  221.78 21.0544 0.0025182 ** 
I(x1 * x2)  1   2.51    2.51  0.2382 0.6403944    
I(x1 * x3)  1   0.61    0.61  0.0581 0.8163964    
I(x2 * x3)  1   0.49    0.49  0.0468 0.8348432    
trt         1   0.02    0.02  0.0019 0.9664292    
Residuals   7  73.74   10.53                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> 
> gasblend.mod2 <- aov(y ~ x1 + x2 + x3 + trt)
> anova(gasblend.mod2)
Analysis of Variance Table

Response: y
          Df Sum Sq Mean Sq F value    Pr(>F)    
x1         1 443.90  443.90 42.1418 0.0003368 ***
x2         1 221.78  221.78 21.0544 0.0025182 ** 
trt        4   3.64    0.91  0.0863 0.9839416    
Residuals  7  73.73   10.53                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> 
> gasblend.mod3 <- aov(y ~ trt)
> anova(gasblend.mod3)
Analysis of Variance Table

Response: y
          Df Sum Sq Mean Sq F value   Pr(>F)   
trt        6 669.32 111.553  10.590 0.003245 **
Residuals  7  73.73  10.534                    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> 
> gasblend.mod4 <- aov(y ~ -1 + x1 + x2 + x3)
> summary.lm(gasblend.mod4)

Call:
aov(formula = y ~ -1 + x1 + x2 + x3)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.0557 -2.2707  0.1793  1.5818  3.9443 

Coefficients:
   Estimate Std. Error t value Pr(>|t|)    
x1  105.116      1.542   68.16 8.41e-16 ***
x2   82.136      1.542   53.26 1.26e-14 ***
x3   95.456      1.542   61.90 2.42e-15 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 2.652 on 11 degrees of freedom
Multiple R-squared: 0.9994,     Adjusted R-squared: 0.9992 
F-statistic:  5923 on 3 and 11 DF,  p-value: < 2.2e-16 

> 
> gasblend.mod5 <- aov(y ~ -1 + x1 + x2 + x3 + I(x1*x2) + I(x1*x3) + I(x2*x3))
> summary.lm(gasblend.mod5)

Call:
aov(formula = y ~ -1 + x1 + x2 + x3 + I(x1 * x2) + I(x1 * x3) + 
    I(x2 * x3))

Residuals:
      Min        1Q    Median        3Q       Max 
-3.991288 -1.834848  0.008712  1.765152  4.008712 

Coefficients:
           Estimate Std. Error t value Pr(>|t|)    
x1          105.791      2.139  49.461 3.09e-11 ***
x2           82.341      2.139  38.498 2.28e-10 ***
x3           95.391      2.139  44.599 7.05e-11 ***
I(x1 * x2)   -5.126      9.832  -0.521    0.616    
I(x1 * x3)   -2.426      9.832  -0.247    0.811    
I(x2 * x3)    2.274      9.832   0.231    0.823    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 3.036 on 8 degrees of freedom
Multiple R-squared: 0.9994,     Adjusted R-squared: 0.999 
F-statistic:  2260 on 6 and 8 DF,  p-value: 1.812e-12 

>