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------------------------------------------------ **Analysis of the Oil Data Set**

A project from Fall 1999 involved heating motor oil until it caught on fire. There were eight runs in random order. Here is the description of the data:

- "conv" stands for conventional oil
- "syn" stands for synthetic oil
- "5/30" and "20/50" are two viscosities
- "time" is the time until catching fire

**Data:**

| Obs | Type | Vis | Time |
|-----|------|-----|------|
| 1 | conv | 5/30 | 345 |
| 2 | syn | 5/30 | 658 |
| 3 | conv | 20/50| 360 |
| 4 | syn | 20/50| 546 |
| 5 | conv | 5/30 | 360 |
| 6 | syn | 5/30 | 676 |
| 7 | conv | 20/50| 342 |
| 8 | syn | 20/50| 512 |

**Task:**

Run the linear model (lm) in Splus or M-Lab to get the ANOVA output using the full model:

\[ \text{model time} = \text{vis} + \text{type} + \text{vis} \times \text{type} \]

1. Determine if there is a mean difference in oil types (conv vs. syn):
- **p-value =**

2. Determine if there is a mean difference in viscosity levels (5/30 vs. 20/50):
- **p-value =**

3. Determine if there is an interaction between the factors:
- **p-value =**

Answer :

Answer:

Check the explanation

Step-by-step explanation:

We shall analyse this in the open source statistical packageR , the complete R snippet is as follows


# read the data into R dataframe

data.df<- read.csv("C:\\Users\\586645\\Downloads\\Chegg\\syn.csv",header=TRUE)

str(data.df)



# perform anova analysis

a<- aov(lm(time~type*vis,data=data.df))


#summarise the results

summary(a)



colr<-c("salmon3" , "plum2","coral1","palegreen1" ,"orangered" ,"magenta4" )

# plots


boxplot(time~type*vis, data=data.df,ylab="Values",

main="Boxplots of the Data",col=colr,horizontal=TRUE)


attach(data.df)

interaction.plot(type,vis,time, type="b", col=c(2:6),

leg.bty="o", leg.bg="beige", lwd=2, pch=c(18,24,22),

xlab="Type",

ylab="Value",

main="Interaction Plot")


The results are


> summary(a)

Df Sum Sq Mean Sq F value Pr(>F)

type 1 121278 121278 478.18 2.59e-05 *** ### significant as the p value is less than 0.05

vis 1 9730 9730 38.36 0.00345 ** ### significant as the p value is less than 0.05

type:vis 1 9316 9316 36.73 0.00374 ** ### significant as the p value is less than 0.05 , hence the interaction effect is significant . The p values are highlighted

Residuals 4 1015 254

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Kindly check the BoxPlot of Data below.

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