Homework 3

1. Exploratory Data Analysis

1.1 Load the mtcars dataset, review its codebook, and report summary statistics for each column. Is there anything you find abnormal?(10pts)

# Load required libraries
library(ggplot2)
library(corrplot)

## corrplot 0.95 loaded

# Load the mtcars dataset
data(mtcars)

# Review the codebook by ?
?mtcars

# Display the first few rows and summary statistics
head(mtcars)

##                    mpg cyl disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
## Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1

summary(mtcars)

##       mpg             cyl             disp             hp       
##  Min.   :10.40   Min.   :4.000   Min.   : 71.1   Min.   : 52.0  
##  1st Qu.:15.43   1st Qu.:4.000   1st Qu.:120.8   1st Qu.: 96.5  
##  Median :19.20   Median :6.000   Median :196.3   Median :123.0  
##  Mean   :20.09   Mean   :6.188   Mean   :230.7   Mean   :146.7  
##  3rd Qu.:22.80   3rd Qu.:8.000   3rd Qu.:326.0   3rd Qu.:180.0  
##  Max.   :33.90   Max.   :8.000   Max.   :472.0   Max.   :335.0  
##       drat             wt             qsec             vs        
##  Min.   :2.760   Min.   :1.513   Min.   :14.50   Min.   :0.0000  
##  1st Qu.:3.080   1st Qu.:2.581   1st Qu.:16.89   1st Qu.:0.0000  
##  Median :3.695   Median :3.325   Median :17.71   Median :0.0000  
##  Mean   :3.597   Mean   :3.217   Mean   :17.85   Mean   :0.4375  
##  3rd Qu.:3.920   3rd Qu.:3.610   3rd Qu.:18.90   3rd Qu.:1.0000  
##  Max.   :4.930   Max.   :5.424   Max.   :22.90   Max.   :1.0000  
##        am              gear            carb      
##  Min.   :0.0000   Min.   :3.000   Min.   :1.000  
##  1st Qu.:0.0000   1st Qu.:3.000   1st Qu.:2.000  
##  Median :0.0000   Median :4.000   Median :2.000  
##  Mean   :0.4062   Mean   :3.688   Mean   :2.812  
##  3rd Qu.:1.0000   3rd Qu.:4.000   3rd Qu.:4.000  
##  Max.   :1.0000   Max.   :5.000   Max.   :8.000

Answer: I don’t find any variable abnormal at this stage. Maybe I will discover some later.

1.2 Provide any ONE visualization you used to understand the data (10pts)

aggregate(mpg ~ cyl, data = mtcars, mean)

##   cyl      mpg
## 1   4 26.66364
## 2   6 19.74286
## 3   8 15.10000

Answer: The less cylinders a model has the the better the miles per gallon.

1.3 Identify at least one trends, correlations, or patterns you find interesting! You can use table or plot to show it. (10pts)

plot(mtcars$wt, mtcars$mpg,
     main = "MPG versus Vehicle Weight",
     xlab = "Weight",
     ylab = "MPG",
     pch = 19,
     col = "blue")

# scatter plot

Answer: The plot shows that the heavier cars have a lower MPG.

1.4 What variables are most strongly correlated with mpg? Answer this with code ALONG WITH markdown narrative. 10pt

mpg_cor <- cor(mtcars)[, "mpg"]
sort(mpg_cor)

##         wt        cyl       disp         hp       carb       qsec       gear 
## -0.8676594 -0.8521620 -0.8475514 -0.7761684 -0.5509251  0.4186840  0.4802848 
##         am         vs       drat        mpg 
##  0.5998324  0.6640389  0.6811719  1.0000000

Answer: The variable most strongly coorelated with mpg is heavier cars and weight at -0.87. Cyl and disp categories are also strong negatives.

1.5 Check whether there are missing data using R codes. If not, show evidence. If yes, which column and how many. 10pts

colSums(is.na(mtcars))

##  mpg  cyl disp   hp drat   wt qsec   vs   am gear carb 
##    0    0    0    0    0    0    0    0    0    0    0

sum(is.na(mtcars))

## [1] 0

Answer: It looks like there are no missing data and every column has a value of zero missing.

1.6 Use Box plot to decide if any variable has significant outliers. 10pts

boxplot(scale(mtcars),
        main = "Boxplots of mtcars Variables",
        las = 2)

outliers <- lapply(mtcars, function(x) boxplot.stats(x)$out)
outliers[lengths(outliers) > 0]

## $hp
## [1] 335
## 
## $wt
## [1] 5.424 5.345
## 
## $qsec
## [1] 22.9
## 
## $carb
## [1] 8

Answer: There are outliers in the colums hp, wt, qsec, and carb.

1.7 Apply range standardization on variable hp, and save it with the new name hp_rs in data.frame mtcars. Report the max and min of the standardized hp_rs to validate. 20pts

mtcars$hp_rs <- (mtcars$hp - min(mtcars$hp)) /
                (max(mtcars$hp) - min(mtcars$hp))

range(mtcars$hp_rs)

## [1] 0 1

Answer: The minimum of hp_rs is 0 and the max is 1.

1.8 Winsorize the variable wt with 5%/95%, save it with the new name wt_win, and report the new max and min. 20pts

limits <- quantile(mtcars$wt, c(0.05, 0.95))

mtcars$wt_win <- pmin(
  pmax(mtcars$wt, limits[1]),
  limits[2]
)

range(mtcars$wt_win)

## [1] 1.73600 5.29275

Answer: After winsorizing the variable, the new min is 1.73600 and the max is 5.29275 . The new variables were saved under wt_win .