Analysis of the oil data set. One project from Fall 1999 consisted of heating mo

Question

Analysis of the oil data set. One project from Fall 1999 consisted of heating motor oil until it catches on fire. There were eight runs in random order where "conv" stands for conventional oil, "syn" stands for synthetic oil, "5/30" and "20/50" are two viscosities, and "time" is the time until catching fire. The data are as follows

Lm>> class vis type Enter model statement Lm>> model time-vis+type+vis*type Sequential Sums of Squares ANOVA Table Source df MS P-val V1S type vis*type Error 1 1 1 4 9730.125 121278.125 9316.125 1014.500 9730.125 121278.125 9316.125 253.625 38.3642 478.1789 36.7319 0.00345430 2.5879e-05 0.00374180 R-square 0.99282 Standard Error 15.9256

Explanation / Answer

we shall do this using the open source statisitcal package R , the complete R snippet is as follows

# read the data into R dataframe
data.df<- read.csv("C:\Users\586645\Downloads\Chegg\conv.csv",header=TRUE)
str(data.df)

# perform anova analysis
a<- aov(lm(Time~ vis*Type,data=data.df))

#summarise the results
summary(a)

colr<-c("slateblue1",
"salmon3" , "plum2","coral1","palegreen1" ,"orangered" ,"magenta4" )
# plots

boxplot(Time~ vis*Type, data=data.df,ylab="Values",
main="Boxplots of the Data",col=colr,horizontal=TRUE)

The results are

> summary(a)
Df Sum Sq Mean Sq F value Pr(>F)
vis 1 9730 9730 38.36 0.00345 **
Type 1 121278 121278 478.18 2.59e-05 ***
vis:Type 1 9316 9316 36.73 0.00374 ** ## interaction effect
Residuals 4 1015 254   
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

The respective p values are highlighted

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