Question 1

To start, we are looking to see if there will be any differences or relationship with the 9 dependent variables and each of the designated groups.

##           Df      Wilks approx F num Df den Df    Pr(>F)    
## Group     11 0.00056105   3.9895     99  208.9 < 2.2e-16 ***
## Residuals 36                                                
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##           Df Pillai approx F num Df den Df    Pr(>F)    
## Group     11 3.3079   1.9019     99    324 1.392e-05 ***
## Residuals 36                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##           Df Hotelling-Lawley approx F num Df den Df    Pr(>F)    
## Group     11           42.972   11.382     99    236 < 2.2e-16 ***
## Residuals 36                                                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##           Df    Roy approx F num Df den Df    Pr(>F)    
## Group     11 34.532   113.01     11     36 < 2.2e-16 ***
## Residuals 36                                            
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Each of the tests show that there are differences in each of the groups. In order to figure out which factors cause these differences, more analysis must be conducted using the other independent variables to see what has a greater impact.

Question 2

For the next test, we were looking to see the relationship between the 9 dependent variables and the dependent variables Contour and Depth as well as the interaction with Contour and Depth.

## 
## Type III MANOVA Tests: Wilks test statistic
##               Df test stat approx F num Df  den Df    Pr(>F)    
## (Intercept)    1  0.008013   385.12      9  28.000 < 2.2e-16 ***
## Depth          3  0.047697     5.60     27  82.417 6.744e-10 ***
## Contour        2  0.211668     3.65     18  56.000 0.0001022 ***
## Depth:Contour  6  0.273274     0.79     54 147.367 0.8382202    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The test shows that each Depth and Contour have importance in describing the dependent variables. Both depth and contour have values below the confidence level of p = .05, but the interaction of the two does not show a difference.

Question 3

Finally, we want to see what the inclusion of Block with our previous independent variables does to the predictability of the dependent variables.

## 
## Type III MANOVA Tests: Wilks test statistic
##               Df test stat approx F num Df  den Df    Pr(>F)    
## (Intercept)    1  0.006336   435.63      9  25.000 < 2.2e-16 ***
## Depth          3  0.028896     6.45     27  73.655 9.554e-11 ***
## Contour        2  0.159872     4.17     18  50.000 3.246e-05 ***
## Block          3  0.079430     3.77     27  73.655 3.347e-06 ***
## Depth:Contour  6  0.216611     0.86     54 132.070    0.7392    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

As the data shows, Block as has a role in predicting the value of the dependent variables. In addition, the p-value for depth, contour, and even their interaction lowered. However, the interaction is still not significant.