title: “MATH1115 Computer Practical Exam”
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subtitle: Semester 2, 2022
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## MY SID IS: XXXXX {-}
## Briefing on Data
The given file, `data.csv`, available on Kaggle, contains information about Audi used cars sold in the U.K. The following data dictionary is reproduced from the source,
– `model`: Audi model.
– `year`: registration year.
– `price`: price in pounds sterling.
– `transmission`: type of gearbox.
– `mileage`: distance used.
– `fuelType`: engine fuel.
– `tax`: road tax.
– `mpg`: miles per gallon.
– `engineSize`: size in litres.
The given file, `data.csv`, is an abridged version of the original dataset, which itself consists of multiple files.
Your task is to help Haochen analyse the `data.csv` data set, using the template provided `XXXXXXXX_MATH1115Final.Rmd`, where `XXXXXXXX` will be replaced by your SID. This template consists of five main sections:
– Initial Data Analysis
– Simple Linear Regression
– Chi-Squared Test
– Binomial Modelling
– Data Wrangling
**How to approach the exam**
1. Attempt all sections.
2. Comment on the code and output (as appropriate).
3. Use `ggplot` for all graphs with appropriate labels and legends. You can choose to use base R, but you will not get full marks.
4. Neatly edit your work, both code and text, before submission.
**Submission**
1. Name your final .Rmd file as `XXXXXXXX_MATH1115Final.Rmd`, where `XXXXXXXX` is your SID.
2. Create the final .html file.
3. Submit your .html and .Rmd files in the MATH1115 Canvas site.
data <- read.csv("data.csv") head(data) names(data) ## INITIAL DATA ANALYSIS **Question 1**: Write a short paragraph on the limitations and ethics associated with this data. **Question 2**: Provide a numerical summary and graphical summary for the variable "price". Write a short paragraph summarising your findings. **Question 3**: For each of the variables "mpg" and "year", provide a graphical summary using ggplot. Write a short paragraph summarising your findings. ## SIMPLE LINEAR REGRESSION **Research Question**: It is to be expected that on average, used cars with greater mileage have a lesser sale price. Haochen claims that for used cars registered in 2009, a negative linear relationship existed between mileage and price. Fit a simple linear regression model and evaluate this claim. Perform any appropriate hypothesis tests and include residual diagnostics. ## CHI-SQUARED TEST **Research Question**: It is claimed that 25% of Audi used cars have automatic transmission, while 40% are manual and a further 35% have semi-automatic transmission. Perform a chi-squared test with \(\ \alpha = 0.05 \)\ to determine the statistical significance of any evidence against this claim. In your answer, use H A T P C. ## BINOMIAL MODELLING Haochen believes that at least half of Audi used cars are diesel, with the remaining half being either petrol driven or else hybrid. i) Verify that in the given data set, 5577 cars are diesel. ii) Model this as sampling from a box model with 10,668 draws with replacement. Calculate the expected value and standard error for the mean of the draws. iii) Comment on your findings, in context. ## DATA WRANGLING Annotate the code below, explaining what each line is doing. ```{r, echo = T, warning = F, message = F, eval = F} select("year") %>%
FLTR <- data$year == 2019
ggplot(data = data[FLTR,], mapping = aes(x = model, y = price)) +
geom_boxplot()
select(transmission, tax) %>%
group_by(transmission) %>%
summarise(tax = mean(tax))
barplot(table(data$transmission), las = 2)
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