You should only use the file Exam_template.Rmd provided on blackboard and you should load this file from your scripts folder / directory.
Save this template as your studentID.Rmd; you will upload this file as your submission. Change the information on line 3 of this file – changing the author information to your student ID. Do not change the authorship to your name.
Ensure that you save your data into your data folder (as discussed in class). You may use the files mypackages.R and helperFunctions.R from blackboard. If you use these files, do not alter them. If you wish to create additional files for custom functions that you have prepared in advance, make sure that you upload these in addition to your .Rmd file and your compiled output file.
Your should knit this file to a document Word format.
Any changes that you make to the data (e.g. variable name changes) should be made entirely within R.
The subsubsections labelled Answer: indicate where you should put in your written Answers. The template also provides blank code chunks for you to complete your Answers; you may choose to add additional chunks if required.
#install.packages(“tidyverse”) #install.packages(“dplyr”) #install.packages(“boot”) #install.packages(“ggplot2”) #install.packages(“psych”) #install.packages(“performance”) #install.packages(“corrplot”) #install.packages(“summarytools”) Having installed all these packages, we shall call the following libraries:
# Load the dataset as follows:
library(readxl)
#data_1=read_excel(file.choose())
# Attach the dataset as follows:
attach(data_1)Error in attach(data_1): object 'data_1' not found# Name the dataset to know how many variables are therein:
names(data_1)Error in eval(expr, envir, enclos): object 'data_1' not found#View(data_1)
dim(data_1)Error in eval(expr, envir, enclos): object 'data_1' not foundThis dataset is part of a larger dataset that has been collected to help to estimate the price of used cars.
It contains the following variables:
You are interested in modelling the price of vehicles that have all of the following properties:
Once you have selected the rows of data with these properties, then you must use the last 4 digits of your studentID to select a random sample of 2000 rows of the data to perform the rest of your analysis with.
You should remove any redundant variables (where only one value remains in that variable).
This subset of the data is what you should use for the rest of this assessment.
(4 marks)
ReCall the libraries
Reading the csv file to the R Studio environmwent
Viewing it to see the dataset
Filtering it accordingly
Saving the filtered dataset to another name of your choice
Selecting a random sample of 2000 rows from the filtered dataset for set.seed = 7889.
Removing the variables with redundant values by running appropriate codes
Converting the variables to factors as appropriate
(7 marks)
data_2 = subset(data_1, transmission=="Manual" & mileage < 90000 & fuelType=="Diesel" & tax < 300, select = -c(fuelType, transmission))Error in subset(data_1, transmission == "Manual" & mileage < 90000 & fuelType == : object 'data_1' not found#View(data_2)
dim(data_2)Error in eval(expr, envir, enclos): object 'data_2' not found#Seeting our seed to be:
set.seed(7889)
data_3 = data_2 %>% sample_n(2000, replace = FALSE)Error in sample_n(., 2000, replace = FALSE): object 'data_2' not found#View(data_3)
dim(data_3)Error in eval(expr, envir, enclos): object 'data_3' not found(2 marks)
Measure of Location: mean, mode, and median. They are useful because they depict where the entire datasets are concentrated.
Measure of Spread: range, interquartile range, variance and standard deviation. They are useful becuase they supplement the information provided by the measure of location.
(4 marks)
summary(data_3)Error in summary(data_3): object 'data_3' not founddescr(data_3)Error in descr(data_3): object 'data_3' not found(4 marks)
In the analysis using measure of central tendency, we observe that the average price (in GB pounds), mileage (total distance covered by the car), annual cost of vehicle tax, miles per gallon, and size of the engine (in litres) are 13933.86, 32538.84,84.97,64.16 and 1.79 respectively, while their median values are 13486, 29666.5, 125, 64.2, and 2. Not only these but also, the modes are 16000 and 11000 for only price (this means that there are bimodal values for the price of the car), 10, 145, 74.3, and 2 are the mode for mileage, tax, mpg, and engineSize. All these talk about measure of central tendency.
Come to think of the measure of variability as used here, the ranges for price (in GB pounds), mileage (total distance covered by the car), annual cost of vehicle tax, miles per gallon, and size of the engine (in litres) are (2395 - 32995), (5 - 89936), (0 - 260), (30.1 - 88.3), and (0.0 - 2.2) respectively. We got 6423.75, 29308, 125, 13.275, and 0.5 as interquartile range values for price (in GB pounds), mileage (total distance covered by the car), annual cost of vehicle tax, miles per gallon, and size of the engine (in litres). Also, the values for variance and standard deviation for each of these variables are (22931232, 4788.657), (445497989, 21106.82), (4263.894, 65.2985), (101.5388, 10.07665), and (0.06297, 0.25094).
(2 marks)
(4 marks)
# To obtain the box plot, run the command below:
# Form the dataset one by one:
price=data_3[,4]; mileage=data_3[,5]; tax=data_3[,6];mpg=data_3[,7];engineSize=data_3[,8]Error in eval(expr, envir, enclos): object 'data_3' not foundError in eval(expr, envir, enclos): object 'data_3' not foundError in eval(expr, envir, enclos): object 'data_3' not foundError in eval(expr, envir, enclos): object 'data_3' not foundError in eval(expr, envir, enclos): object 'data_3' not found#Produce the data frame:
data_4 = data.frame(price, mileage, tax, mpg, engineSize)Error in data.frame(price, mileage, tax, mpg, engineSize): object 'price' not found#Draw the plot:
boxplot(data_4, main="Box-Whisker Plot", col=c(1:8), col.main=2, pch=22, las=1, sub="Fig. I", col.sub="chocolate")Error in boxplot(data_4, main = "Box-Whisker Plot", col = c(1:8), col.main = 2, : object 'data_4' not found# To obtain the histogram, run the commands below:
h=hist(price, main="Histigram", sub="Figire 2", col.sub="blue2",col=c(1:8), xlab="Price", col.main="yellow4")Error in hist(price, main = "Histigram", sub = "Figire 2", col.sub = "blue2", : object 'price' not foundh=hist(mileage, main="Histigram", sub="Figire 3", col.sub="blue2",col=c(1:8), xlab="Mileage", col.main="yellow4")Error in hist(mileage, main = "Histigram", sub = "Figire 3", col.sub = "blue2", : object 'mileage' not foundh=hist(tax, main="Histigram", sub="Figire 4", col.sub="blue2",col=c(1:8), xlab="Tax", col.main="yellow4")Error in hist(tax, main = "Histigram", sub = "Figire 4", col.sub = "blue2", : object 'tax' not foundh=hist(mpg, main="Histigram", sub="Figire 5", col.sub="blue2",col=c(1:8), xlab="mpg", col.main="yellow4")Error in hist.default(mpg, main = "Histigram", sub = "Figire 5", col.sub = "blue2", : 'x' must be numerich=hist(engineSize, main="Histigram", sub="Figire 6", col.sub="blue2",col=c(1:8), xlab="engineSize", col.main="yellow4")Error in hist(engineSize, main = "Histigram", sub = "Figire 6", col.sub = "blue2", : object 'engineSize' not found# To obtain the SCATTER PLOT, run the commands below:
plot(mileage,price, main="Scatter Plot", col.main=2, sub="Figure 7", col.sub="green", xlab="Mileage", ylab="Price", col.lab="blue", pch=19, col=c(1:22), las=1)Error in plot(mileage, price, main = "Scatter Plot", col.main = 2, sub = "Figure 7", : object 'mileage' not foundplot(tax,price, main="Scatter Plot", col.main=2, sub="Figure 8", col.sub="green", xlab="tax", ylab="Price", col.lab="blue", pch=19, col=c(1:22), las=1)Error in plot(tax, price, main = "Scatter Plot", col.main = 2, sub = "Figure 8", : object 'tax' not foundplot(mpg,price, main="Scatter Plot", col.main=2, sub="Figure 9", col.sub="green", xlab="mpg", ylab="Price", col.lab="blue", pch=19, col=c(1:22), las=1)Error in pairs.default(data.matrix(x), ...): object 'price' not foundplot(engineSize,price, main="Scatter Plot", col.main=2, sub="Figure 10", col.sub="green", xlab="EngineSize", ylab="Price", col.lab="blue", pch=19, col=c(1:22), las=1)Error in plot(engineSize, price, main = "Scatter Plot", col.main = 2, : object 'engineSize' not foundIn Box Plot, it appears that mileage appears to be a bit normal while others are away from normality.
The Histogram and scatter plots also show similar illustrations.
cor(data_4)Error in is.data.frame(x): object 'data_4' not foundmodel = lm(price ~ mileage, data = data_4)Error in is.data.frame(data): object 'data_4' not foundsummary(model)Error in summary(model): object 'model' not foundplot(mileage,price, main="Scatter Plot", col.main=2, sub="", col.sub="green", xlab="Mileage", ylab="Price", col.lab="blue", pch=19, col="chocolate", las=1)Error in plot(mileage, price, main = "Scatter Plot", col.main = 2, sub = "", : object 'mileage' not foundabline(coef(model), lwd=3, col=1)Error in coef(model): object 'model' not foundlibrary(performance)
model_performance(model)Error in model_performance(model): object 'model' not foundanova(model)Error in anova(model): object 'model' not foundmodel2 = step(model)Error in terms(object): object 'model' not found#Set up the bootstrap as follows:
# function to obtain R-Squared from the data:
set.seed(7889)
library(boot)
#Define function to calculate R-squared value
rsq_function = function(formula, data, indices) {
w = data[indices,]
fit = lm(formula, data=w)
return(summary(fit)$r.square)
}
#perform bootstrapping with 2000 replications
rw = boot(data=data_4, statistic=rsq_function, R=2000, formula=price~mileage)Error in NROW(data): object 'data_4' not found#view results of boostrapping
rwError in eval(expr, envir, enclos): object 'rw' not found#plot(rw)
#To calculate the 95% confidence interval for the estimated R-squared of the model:
#To calculate adjusted bootstrap percentile (bca) interval:
boot.ci(rw, type="bca")Error in boot.ci(rw, type = "bca"): object 'rw' not foundThe remaining explanatory variables are tax, mpg, and engineSize:
model3 = lm(price ~ tax + + mpg + engineSize - 1, data = data_4)Error in is.data.frame(data): object 'data_4' not foundsummary(model3)Error in summary(model3): object 'model3' not foundanova(model3)Error in anova(model3): object 'model3' not foundIt is obvious, from the results, that all the three remaining explanatory variables are statistically significant at 0.05 level of significance. Also, the results for the multiple R-squared and Adjusted multiple R-squared (0.9317 and 0.9316) show that there are 93% variations in price which are explained by all the three erxplanatory variables.
(4 marks)
library(performance)
model_performance(model3)Error in model_performance(model3): object 'model3' not found# For normality assumption:
residual=resid(model3)Error in resid(model3): object 'model3' not found## Breusch-Pagan Test for Heteroscedasticity Assumption
library(lmtest)Loading required package: zoo
Attaching package: 'zoo'The following objects are masked from 'package:base':
as.Date, as.Date.numericbptest(model3, studentize=FALSE)Error in bptest(model3, studentize = FALSE): object 'model3' not foundThe result shows that multiple R-squared is approximately 93% which tells us that 0nly 93% variations are explained by the explanatory variables.
The model is likely to develop a problem becuase it is not stable.
The best for this scenario is maximal model beacuse it is more accurate and adequate.
A client is looking to purchase a used Skoda Superb (registration year either 2018 or 2019, manual transmission, diesel engine) and wants to understand what factors influence the expected price of a used car, (and how they influence the price).
Write a short report of 300-500 words for the client.
Furthermore, include an explanation as to which statistical model you would recommend, and why you have selected that statistical model.
Comment on any suggestions for alterations to the statistical model that would be appropriate to consider.
Highlight what may or may not be directly transferable from the scenario analysed in Questions 1 to 5.
A client who wants to buy to a used Skoda Superb (registration year either 2018 or 2019, manual transmission, diesel engine) car would need to understand that some basic factors such as brand, model, fuel type, and tax would influence the expected price of a used car. In the first instance, someone who needs Audi will know that its price will surely be different (either less or more than) from the price of another brand, say BMW. Also, the model of the car will determine its price. It is expected that Audi with model A4 will be different in price while comparing it with BWM of model X3. The type of the fuel a car uses determines the price of such a car. In this scenario, you cannot expect a car using diesel to be at the same price with that of a car using petrol. Also, annual cost of vehicle tax influences its price.
I would like to recommend that a multiple linear regression model of price connecting with brand, model, fuel type, and tax be used because of the roles played by all these explanatory variables in explaining the price of this used car.
However, it is a good idea to suggest that some modifications should be made to our previous models such that the new model can be captured or incorporated into our analysis.
From the scenario analyzed in Questions 1 - 5, mileage less tha 90000 may not be transferable while manual transmission, diesel engine, and cost less than 300 Euro are transferable.
Do not edit this part. Make sure that you compile your document so that the information about your session (including software / package versions) is included in your submission.
sessionInfo()R version 4.2.0 (2022-04-22 ucrt)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 22000)
Matrix products: default
locale:
[1] LC_COLLATE=English_United States.utf8
[2] LC_CTYPE=English_United States.utf8
[3] LC_MONETARY=English_United States.utf8
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.utf8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] lmtest_0.9-40 zoo_1.8-10 readxl_1.4.0 summarytools_1.0.1
[5] corrplot_0.92 performance_0.9.1 psych_2.2.5 boot_1.3-28
[9] forcats_0.5.1 stringr_1.4.0 dplyr_1.0.9 purrr_0.3.4
[13] readr_2.1.2 tidyr_1.2.0 tibble_3.1.7 ggplot2_3.3.6
[17] tidyverse_1.3.1
loaded via a namespace (and not attached):
[1] httr_1.4.3 sass_0.4.1 jsonlite_1.8.0 modelr_0.1.8
[5] bslib_0.3.1 assertthat_0.2.1 pander_0.6.5 cellranger_1.1.0
[9] yaml_2.3.5 pillar_1.7.0 backports_1.4.1 lattice_0.20-45
[13] glue_1.6.2 digest_0.6.29 pryr_0.1.5 checkmate_2.1.0
[17] rvest_1.0.2 colorspace_2.0-3 plyr_1.8.7 htmltools_0.5.2
[21] pkgconfig_2.0.3 broom_1.0.0 haven_2.5.0 magick_2.7.3
[25] scales_1.2.0 tzdb_0.3.0 generics_0.1.3 ellipsis_0.3.2
[29] withr_2.5.0 cli_3.3.0 mnormt_2.1.0 magrittr_2.0.3
[33] crayon_1.5.1 evaluate_0.15 fs_1.5.2 fansi_1.0.3
[37] nlme_3.1-158 MASS_7.3-57 xml2_1.3.3 rapportools_1.1
[41] tools_4.2.0 hms_1.1.1 lifecycle_1.0.1 matrixStats_0.62.0
[45] munsell_0.5.0 reprex_2.0.1 compiler_4.2.0 jquerylib_0.1.4
[49] rlang_1.0.4 grid_4.2.0 rstudioapi_0.13 tcltk_4.2.0
[53] base64enc_0.1-3 rmarkdown_2.14 gtable_0.3.0 codetools_0.2-18
[57] DBI_1.1.3 reshape2_1.4.4 R6_2.5.1 lubridate_1.8.0
[61] knitr_1.39 fastmap_1.1.0 utf8_1.2.2 insight_0.18.0
[65] stringi_1.7.8 parallel_4.2.0 Rcpp_1.0.9 vctrs_0.4.1
[69] dbplyr_2.2.1 tidyselect_1.1.2 xfun_0.31