Lab Report 5

Question 1

Name the factors and level (2M)

Factor : Time
High : 18
Low : 12
Factor : Culture Medium
High : 2
Low : 1

Fill in the table 6(3M)

knitr::include_graphics("D://UMP//Sem 5//EDA//Lab//Lab Report 5.PNG")

A <- rep(c(-1,1),2)
B <- rep(c(-1,-1,1,1),1)

growth <- c(21,37,25,31,22,39,26,34,23,38,24,29,28,38,25,33,20,35,29,30,26,36,27,35)
data <- data.frame(A,B,growth)
data

results <- lm(growth ~ A+B+A:B, data)

summary(results)

## 
## Call:
## lm(formula = growth ~ A + B + A:B, data = data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -3.333 -1.500 -0.250  1.208  4.667 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  29.6250     0.4614  64.213  < 2e-16 ***
## A             4.9583     0.4614  10.747 9.29e-10 ***
## B            -0.6250     0.4614  -1.355 0.190617    
## A:B          -1.9583     0.4614  -4.245 0.000397 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.26 on 20 degrees of freedom
## Multiple R-squared:  0.8713, Adjusted R-squared:  0.852 
## F-statistic: 45.12 on 3 and 20 DF,  p-value: 4.346e-09

anova(results)

Question 4

a)

State the hypothesis, the pvalue, decision by comparing p-value and significance level, and conclusion. (2M)

\(H{0}\): All population means are equal @ no treatment effects
\(H{1}\): At least one of the population means is different @ there is treatment effects
\(p-value = 0.0004\))\(<\)(\(\alpha=0.05\)),we reject \(H{0}\).
At \(\alpha=0.05\), At least one of the population means is different

b)

State the significant factor

The significant factor is factor A

results$effects

##   (Intercept)             A             B           A:B               
## -145.13226726  -24.29077328    3.06186218    9.59383483   -0.95905614 
##                                                                       
##    2.02916059    0.43740888    2.59204930    0.04094386    1.02916059 
##                                                                       
##   -1.56259112   -2.40795070    5.04094386    1.02916059   -0.56259112 
##                                                                       
##    1.59204930   -2.95905614   -1.97083941    3.43740888   -1.40795070 
##                                                         
##    3.04094386   -0.97083941    1.43740888    3.59204930

effects <- abs(results$effects[-1])
qq <- qqnorm(effects)
text(qq$x, qq$y, labels = names(effects))

The normal probability plot shows that factor A and Factor A and B is significant. Factor B is not approximately on a straight line.

library(gplots)

## Warning: package 'gplots' was built under R version 4.0.5

## 
## Attaching package: 'gplots'

## The following object is masked from 'package:stats':
## 
##     lowess

plotmeans(growth~data$B,xlab="factor B",ylab="tool growth", main="Effect Plot",barcol="yellow")

plotmeans(growth~data$A,xlab="factor A",ylab="tool growth", main="Effect Plot",barcol="green")

Factor B : The main effect plot shows that there is no main effect exist for factor B.Because, factor B is not significant.
Factor A : The main effect plot shows that there is main effect exist for factor A.Because, factor A is significant.

interaction.plot(x.factor = data$A, #x-axis variable
trace.factor = data$B, #variable for lines
response = data$growth, #y-axis variable
fun = median, #metric to plot
ylab = "yield",
xlab = "A",
col = c("pink", "blue"),
lty = 1, #line type
lwd = 2, #line width
trace.label = "B")

C)

Comment the main and interaction plot.(2M)

Interaction plot : The interaction plot shows that there is interaction between factor A and B. because there is an intersect between the line.