Lab Report 4
Mohamad Nadzman Bin Mohd Amin
12/8/2021
library(readr)
data <- read_csv("D:/UMP/Sem 5/EDA/Lab Report/Lab Report 4.csv")##
## -- Column specification --------------------------------------------------------
## cols(
## manufacturer = col_character(),
## process = col_character(),
## brightness = col_double()
## )data## # A tibble: 45 x 3
## manufacturer process brightness
## <chr> <chr> <dbl>
## 1 Kodak A 32
## 2 Kodak B 26
## 3 Kodak C 28
## 4 Kodak A 34
## 5 Kodak B 29
## 6 Kodak C 28
## 7 Kodak A 31
## 8 Kodak B 27
## 9 Kodak C 27
## 10 Kodak A 30
## # ... with 35 more rows(i) What is the independent and dependent variable?
- Independent: Manufacturers and development process
- Dependent: Brightness of film produced
(ii) Identify the number of treatments and list all the treatment
- A = 3, B = 3, k=treatments k= a * b = 3 * 3 = 9
- Number of treatments : 9
- Kodak A, Kodak B, Kodak C, Fuji A, Fuji B, Fuji C, Konica A, Konica B, Konica C
(iii) Write down the model for the experiment
knitr::include_graphics("D:/UMP/Sem 5/EDA/Lab Report/model of two factor factorial.PNG")
(iv) Perform the statistical analysis for the experiment.
A=as.factor(data$manufacturer)
B=as.factor(data$process)
results=aov(brightness ~ A * B, data = data)
summary(results)## Df Sum Sq Mean Sq F value Pr(>F)
## A 2 1363.4 681.7 117.31 < 2e-16 ***
## B 2 165.6 82.8 14.25 2.76e-05 ***
## A:B 4 247.0 61.8 10.63 8.63e-06 ***
## Residuals 36 209.2 5.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1knitr::include_graphics("D:/UMP/Sem 5/EDA/Lab Report/anova lab report 4.png")
(v) Conduct and comment on the model adequacy checking
residuals <- resid(results)
residuals## 1 2 3 4 5 6
## -8.00000e-01 -2.60000e+00 -1.00000e+00 1.20000e+00 4.00000e-01 -1.00000e+00
## 7 8 9 10 11 12
## -1.80000e+00 -1.60000e+00 -2.00000e+00 -2.80000e+00 1.40000e+00 1.00000e+00
## 13 14 15 16 17 18
## 4.20000e+00 2.40000e+00 3.00000e+00 -2.00000e+00 -4.80000e+00 -1.80000e+00
## 19 20 21 22 23 24
## -4.00000e+00 1.20000e+00 -1.80000e+00 -1.00000e+00 1.20000e+00 2.20000e+00
## 25 26 27 28 29 30
## 5.00000e+00 3.20000e+00 1.20000e+00 2.00000e+00 -8.00000e-01 2.00000e-01
## 31 32 33 34 35 36
## -8.00000e-01 2.00000e-01 -7.21645e-16 2.00000e-01 3.20000e+00 2.00000e+00
## 37 38 39 40 41 42
## 1.20000e+00 -1.80000e+00 1.00000e+00 -2.80000e+00 -1.80000e+00 -3.00000e+00
## 43 44 45
## 2.20000e+00 2.00000e-01 -7.21645e-16predicted <- predict(results)
predicted## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
## 32.8 28.6 29.0 32.8 28.6 29.0 32.8 28.6 29.0 32.8 28.6 29.0 32.8 28.6 29.0 45.0
## 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
## 36.8 33.8 45.0 36.8 33.8 45.0 36.8 33.8 45.0 36.8 33.8 45.0 36.8 33.8 23.8 26.8
## 33 34 35 36 37 38 39 40 41 42 43 44 45
## 25.0 23.8 26.8 25.0 23.8 26.8 25.0 23.8 26.8 25.0 23.8 26.8 25.0library(ggpubr)## Warning: package 'ggpubr' was built under R version 4.0.5## Loading required package: ggplot2## Warning: package 'ggplot2' was built under R version 4.0.5shapiro.test(residuals)##
## Shapiro-Wilk normality test
##
## data: residuals
## W = 0.98732, p-value = 0.8981knitr::include_graphics("D:/UMP/Sem 5/EDA/Lab Report/shapiro wilk test.PNG")
plot(predicted, residuals)
plot(lm(residuals~predicted))
- The model is good for constant variance because the points is scattered randomly above and below the reference line.
library(car)## Warning: package 'car' was built under R version 4.0.5## Loading required package: carDatadurbinWatsonTest(results)## lag Autocorrelation D-W Statistic p-value
## 1 0.4294455 1.13805 0.008
## Alternative hypothesis: rho != 0knitr::include_graphics("D:/UMP/Sem 5/EDA/Lab Report/Independent test.PNG")
- Since the test is exist correlation in residuals, the data is not independence.
knitr::include_graphics("D:/UMP/Sem 5/EDA/Lab Report/Marking Files.png")
knitr::include_graphics("D:/UMP/Sem 5/EDA/Lab Report/Rubrics.PNG")