> conv.mod1a <- aov(pctconv_a ~ x1_a + x2_a)
> anova(conv.mod1a)
Analysis of Variance Table

Response: pctconv_a
          Df Sum Sq Mean Sq F value    Pr(>F)    
x1_a       1    256     256     Inf < 2.2e-16 ***
x2_a       1     64      64     Inf < 2.2e-16 ***
Residuals  1      0       0                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
Warning message:
In anova.lm(conv.mod1a) :
  ANOVA F-tests on an essentially perfect fit are unreliable
> summary.lm(conv.mod1a)

Call:
aov(formula = pctconv_a ~ x1_a + x2_a)

Residuals:
1 2 3 4 
0 0 0 0 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)       20          0     Inf   <2e-16 ***
x1_a               8          0     Inf   <2e-16 ***
x2_a               4          0     Inf   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 0 on 1 degrees of freedom
Multiple R-squared:     1,      Adjusted R-squared:     1 
F-statistic:   Inf on 2 and 1 DF,  p-value: < 2.2e-16 

> 
> conv.mod2a <- aov(pctconv_a ~ x1_a + x2_a + I(x1_a*x2_a))
> anova(conv.mod2a)
Analysis of Variance Table

Response: pctconv_a
               Df Sum Sq Mean Sq F value Pr(>F)
x1_a            1    256     256               
x2_a            1     64      64               
I(x1_a * x2_a)  1      0       0               
Residuals       0      0                       
Warning message:
In anova.lm(conv.mod2a) :
  ANOVA F-tests on an essentially perfect fit are unreliable
> summary.lm(conv.mod2a)

Call:
aov(formula = pctconv_a ~ x1_a + x2_a + I(x1_a * x2_a))

Residuals:
ALL 4 residuals are 0: no residual degrees of freedom!

Coefficients:
               Estimate Std. Error t value Pr(>|t|)
(Intercept)          20         NA      NA       NA
x1_a                  8         NA      NA       NA
x2_a                  4         NA      NA       NA
I(x1_a * x2_a)        0         NA      NA       NA

Residual standard error: NaN on 0 degrees of freedom
Multiple R-squared:     1,      Adjusted R-squared:   NaN 
F-statistic:   NaN on 3 and 0 DF,  p-value: NA 

> 
> 
> 
> conv.mod1 <- aov(pctconv ~ x1 + x2)
> anova(conv.mod1)
Analysis of Variance Table

Response: pctconv
          Df Sum Sq Mean Sq F value    Pr(>F)    
x1         1    256   256.0  71.111 0.0003847 ***
x2         1     64    64.0  17.778 0.0083569 ** 
Residuals  5     18     3.6                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> summary.lm(conv.mod1)

Call:
aov(formula = pctconv ~ x1 + x2)

Residuals:
         1          2          3          4          5          6          7 
-1.000e+00 -1.000e+00 -1.000e+00 -1.000e+00  8.506e-16  2.000e+00 -1.000e+00 
         8 
 3.000e+00 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  21.0000     0.6708  31.305 6.24e-07 ***
x1            8.0000     0.9487   8.433 0.000385 ***
x2            4.0000     0.9487   4.216 0.008357 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 1.897 on 5 degrees of freedom
Multiple R-squared: 0.9467,     Adjusted R-squared: 0.9254 
F-statistic: 44.44 on 2 and 5 DF,  p-value: 0.0006545 

> 
> conv.mod2 <- aov(pctconv ~ x1 + x2 + I(x1^2) + I(x2^2) + I(x1*x2))
> anova(conv.mod2)
Analysis of Variance Table

Response: pctconv
           Df Sum Sq Mean Sq   F value   Pr(>F)   
x1          1    256 256.000      76.8 0.003129 **
x2          1     64  64.000      19.2 0.022006 * 
I(x1^2)     1      8   8.000       2.4 0.219102   
I(x1 * x2)  1      0   0.000 1.709e-30 1.000000   
Residuals   3     10   3.333                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> summary.lm(conv.mod2)

Call:
aov(formula = pctconv ~ x1 + x2 + I(x1^2) + I(x2^2) + I(x1 * 
    x2))

Residuals:
 1  2  3  4  5  6  7  8 
 0  0  0  0 -1  1 -2  2 

Coefficients: (1 not defined because of singularities)
              Estimate Std. Error   t value Pr(>|t|)    
(Intercept)  2.200e+01  9.129e-01    24.100 0.000157 ***
x1           8.000e+00  9.129e-01     8.764 0.003129 ** 
x2           4.000e+00  9.129e-01     4.382 0.022006 *  
I(x1^2)     -2.000e+00  1.291e+00    -1.549 0.219102    
I(x1 * x2)  -1.193e-15  9.129e-01 -1.31e-15 1.000000    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 1.826 on 3 degrees of freedom
Multiple R-squared: 0.9704,     Adjusted R-squared: 0.931 
F-statistic:  24.6 on 4 and 3 DF,  p-value: 0.01250 

>