Q 13

Set up

obs <-c(25
    
,
19
    
,
15
    
,
15
    
,
29
    
,
23
    
,
28
    
,
35
    
,
24
    
,
35
    
,
38
    
,
25,
30
    
,
28
    
,
17
    
,
16
    
,
27
    
,
24
    
,
21
    
,
27
    
,
25
    
,
21
    
,
34
,   

29,
26
    
,
20
    
,
14
    
,
13
    
,
24
    
,
21
    
,
27
    
,
25
    
,
20
    
,
24
    
,
30
    

,33
)

Batch <- c(rep(seq(1,4),9))
process<- c(rep(1,4),rep(2,4),rep(3,4),rep(1,4),rep(2,4),rep(3,4),rep(1,4),rep(2,4),rep(3,4))

A state model equation

This is a nested design so

\[y= \mu+a_i+a(b)_i_j+error\]

B

We are testing to see if process has an effect on burn rates. Null is that there is no effect, alt is that there is.

library(GAD)

## Warning: package 'GAD' was built under R version 4.1.3

## Loading required package: matrixStats

## Warning: package 'matrixStats' was built under R version 4.1.3

## Loading required package: R.methodsS3

## Warning: package 'R.methodsS3' was built under R version 4.1.3

## R.methodsS3 v1.8.2 (2022-06-13 22:00:14 UTC) successfully loaded. See ?R.methodsS3 for help.

Batch <- as.random(Batch)
process<- as.fixed(process)
model <- lm(obs~process+Batch%in%process)
gad(model)

## Analysis of Variance Table
## 
## Response: obs
##               Df Sum Sq Mean Sq F value   Pr(>F)   
## process        2 446.06 223.028  3.5365 0.073563 . 
## process:Batch  9 567.58  63.065  4.1965 0.002349 **
## Residual      24 360.67  15.028                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Part C

From running the nested model, the main effect of process appears to not be significant but there is a significant interaction between the burn rate and the batch it was collected from at a significance of .05.