Topic: Sephora Beauty Website’s Rating and Product Analysis

Dataset: Sephore Website Data

Owner: Raghad Alharbi

Source: Kaggle.com

Data dictionary can be found at: https://www.kaggle.com/datasets/raghadalharbi/all-products-available-on-sephora-website

The variables included in this entire data set are the following: id, brand, category, name, size, rating, number of reviews, love, price, value price, URL, marketing flags, ingredients, online only, exclusive, limited edition, limited time offer.

  1. Data

What data set are you planning to use? Source, URL, size, description I plan on using the Sephora Website Dataset from Kaggle. The original owner is …. She/he was able to gather all the data by scraping the Sephora Website for variables such as size, love, rating, the number of customers who left reviews, ingredients, brand, name, and category. This dataset contains 9800 observations and 21 variables.

Does it contain both quantitative and categorical values? My data does contain both quantitative and categorical values. Quantitative values include price, rating, love, number of reviews, and value price. The categorical values include brand, name, category, and ingredients.

Does it have any personal importance for you? I wouldn’t say this project has had any personal importance to me other than simply loving to purchase and apply make-up! My mother went to cosmetology school and made money doing hair when I grew up and that was the only job where she and I could spend a lot of time together. I was surprised to learn that Sephora Beauty carries so many brands online than they do in the physical store, so I had a lot of data to work with.

—————— Loading Libraries ———————

#We will beging loading the packages we will need for this project.

library(tidyverse)
## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --
## v ggplot2 3.3.5     v purrr   0.3.4
## v tibble  3.1.6     v dplyr   1.0.8
## v tidyr   1.2.0     v stringr 1.4.0
## v readr   2.1.2     v forcats 0.5.1
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
library(dplyr) #to wrangle out data
library(ggplot2) #for plottinf our data
library(RColorBrewer) #adding some color 
## Warning: package 'RColorBrewer' was built under R version 4.1.3

———— Readind data……. ————–

library(readr)
sephora_website_dataset <- read_csv("sephora_website_dataset.csv")
## Rows: 9168 Columns: 21
## -- Column specification --------------------------------------------------------
## Delimiter: ","
## chr (10): brand, category, name, size, URL, MarketingFlags_content, options,...
## dbl (10): id, rating, number_of_reviews, love, price, value_price, online_on...
## lgl  (1): MarketingFlags
## 
## i Use `spec()` to retrieve the full column specification for this data.
## i Specify the column types or set `show_col_types = FALSE` to quiet this message.
sephora_website_dataset
## # A tibble: 9,168 x 21
##         id brand        category name  size  rating number_of_revie~  love price
##      <dbl> <chr>        <chr>    <chr> <chr>  <dbl>            <dbl> <dbl> <dbl>
##  1 2218774 Acqua Di Pa~ Fragran~ Blu ~ 5 x ~    4                  4  3002    66
##  2 2044816 Acqua Di Pa~ Cologne  Colo~ 0.7 ~    4.5               76  2700    66
##  3 1417567 Acqua Di Pa~ Perfume  Aran~ 5 oz~    4.5               26  2600   180
##  4 1417617 Acqua Di Pa~ Perfume  Mirt~ 2.5 ~    4.5               23  2900   120
##  5 2218766 Acqua Di Pa~ Fragran~ Colo~ 5 x ~    3.5                2   943    72
##  6 1417609 Acqua Di Pa~ Perfume  Fico~ 5 oz~    4.5               79  2600   180
##  7 1638832 Acqua Di Pa~ Perfume  Rosa~ 3.4 ~    4.5               79  5000   210
##  8 1284462 Acqua Di Pa~ Cologne  Colo~ 1.7 ~    5                 13   719   120
##  9 2221588 Acqua Di Pa~ Body Mi~ Peon~ 1.7o~    4                  5   800    58
## 10 2221596 Acqua Di Pa~ Perfume  Rosa~ 1.7o~    3                  5  2100    58
## # ... with 9,158 more rows, and 12 more variables: value_price <dbl>,
## #   URL <chr>, MarketingFlags <lgl>, MarketingFlags_content <chr>,
## #   options <chr>, details <chr>, how_to_use <chr>, ingredients <chr>,
## #   online_only <dbl>, exclusive <dbl>, limited_edition <dbl>,
## #   limited_time_offer <dbl>

———- Battle of the Doctor Brands: Moisturizer Edition ——————

I selected 8 variables from this data set, and then I began filtering using the filter() function from the dplyr package of four different Doctor-owned brands in Sephora. These brands carried so many different products to work with such as face washes, face serums, face masks, sunscreen, and other specialty products.

  1. Questions

What questions are you considering? 1. I want to see if there is a relationship between price points and product size. 2. I would also like to see if there is a relationship between price point and brand rating 3. I want to see what facial product had the highest rating and look at the cost 4. I want to see what product was the most popular – use a frequency table 5. I want to filter the data and look to see which brand had the best-rated face serum, face wash, and moisturizer.

BOD <- sephora_website_dataset %>%
  select(brand, category, price, name, number_of_reviews, love, rating, size, value_price) %>%
  filter(brand %in% c("Dr Roebuck's", "Dr. Barbara Sturm", "Dr. Brandt Skincare", "Dr. Dennis Gross Skincare", "Dr. Jart+")) %>%
  filter(category %in% c("Face Wash & Cleansers", "Face Serums", "Face Masks", "Toners", "Moisturizers")) %>%
  group_by(category)

BOD
## # A tibble: 105 x 9
## # Groups:   category [5]
##    brand    category price name  number_of_revie~  love rating size  value_price
##    <chr>    <chr>    <dbl> <chr>            <dbl> <dbl>  <dbl> <chr>       <dbl>
##  1 Dr Roeb~ Moistur~    45 No W~              236  5300    4   1.69~          45
##  2 Dr Roeb~ Face Ma~    28 Ulur~               28  4200    4.5 1.69~          28
##  3 Dr Roeb~ Face Se~    60 Perk~               37  2200    4   1 oz~          60
##  4 Dr Roeb~ Face Ma~    28 Tama~               15  3000    4   1.69~          28
##  5 Dr Roeb~ Face Ma~    28 Iceb~                8  1600    4   1.69~          28
##  6 Dr Roeb~ Face Se~    60 True~               22  1900    4.5 1 oz~          60
##  7 Dr Roeb~ Face Wa~    25 Noos~               37  1300    4   3.38~          25
##  8 Dr Roeb~ Moistur~    45 Stok~                3   272    4   1.69~          45
##  9 Dr Roeb~ Face Wa~    25 Kibo~                6   772    4   3.38~          25
## 10 Dr Roeb~ Face Se~    60 Surf~               16   782    4   1 oz~          60
## # ... with 95 more rows

Calculate the Missing Values: Using the sum() function

sum(is.na(BOD))
## [1] 0
(sum (is.na (BOD))/prod (dim (BOD)))*100
## [1] 0

Variance:

var.test(BOD$value_price, BOD$price) #As the p value is greater than 0.05, there is no evidence to suggest that the variances are unequal
## 
##  F test to compare two variances
## 
## data:  BOD$value_price and BOD$price
## F = 0.99926, num df = 104, denom df = 104, p-value = 0.997
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.6789316 1.4707262
## sample estimates:
## ratio of variances 
##           0.999261
varttest <- t.test(BOD$value_price, BOD$price, var.equal = TRUE)

head(varttest) #I prefer this format/view
## $statistic
##           t 
## 0.006690631 
## 
## $parameter
##  df 
## 208 
## 
## $p.value
## [1] 0.9946681
## 
## $conf.int
## [1] -22.37379  22.52617
## attr(,"conf.level")
## [1] 0.95
## 
## $estimate
## mean of x mean of y 
##  84.75238  84.67619 
## 
## $null.value
## difference in means 
##                   0

Welch Two Sample T-Test: A two sample t test is used to test the null hypothesis that the two samples come from distributions with the same mean (i.e. the means are not different)

pairedtwosampletest <- t.test(BOD$value_price, BOD$price, paired= TRUE)

head(pairedtwosampletest) #I prefer this format/view 
## $statistic
##        t 
## 1.421062 
## 
## $parameter
##  df 
## 104 
## 
## $p.value
## [1] 0.1582902
## 
## $conf.int
## [1] -0.0301304  0.1825114
## attr(,"conf.level")
## [1] 0.95
## 
## $estimate
## mean of the differences 
##              0.07619048 
## 
## $null.value
## difference in means 
##                   0

Chi-Square Testing: Two Categorical Variables

BOD2 <- sephora_website_dataset %>%
  select(brand, category, price, name, MarketingFlags_content, details, ingredients, rating) %>%
  filter(brand %in% c("Dr Roebuck's", "Dr. Barbara Sturm", "Dr. Brandt Skincare", "Dr. Dennis Gross Skincare", "Dr. Jart+")) %>%
  filter(category %in% c("Face Serums", "Toners", "Moisturizers")) %>%
  filter(rating > 4.0)

BOD2
## # A tibble: 26 x 8
##    brand        category price name  MarketingFlags_~ details ingredients rating
##    <chr>        <chr>    <dbl> <chr> <chr>            <chr>   <chr>        <dbl>
##  1 Dr Roebuck's Face Se~    60 True~ exclusive · onl~ "What ~ "-Hyaluron~    4.5
##  2 Dr Roebuck's Toners      28 Life~ exclusive · onl~ "What ~ "-Glycolic~    4.5
##  3 Dr. Barbara~ Moistur~   230 Face~ 0                "What ~ "-Skullcap~    4.5
##  4 Dr. Barbara~ Face Se~   145 Anti~ 0                "What ~ "-Hyaluron~    5  
##  5 Dr. Barbara~ Face Se~   310 Nigh~ online only      "What ~ "-Extracts~    4.5
##  6 Dr. Barbara~ Face Se~   300 Dark~ 0                "What ~ "-Hyaluron~    5  
##  7 Dr. Barbara~ Moistur~   215 Clar~ 0                "What ~ "-Complex ~    4.5
##  8 Dr. Barbara~ Face Se~    55 Clar~ 0                "What ~ "-Complex ~    5  
##  9 Dr. Barbara~ Moistur~   205 Face~ 0                "What ~ "-Purslane~    4.5
## 10 Dr. Barbara~ Moistur~   230 Brig~ 0                "What ~ "-Extract ~    5  
## # ... with 16 more rows

Chi-Square T-Test

chiqSB <- chisq.test(BOD2$brand, BOD2$MarketingFlags_content)
## Warning in chisq.test(BOD2$brand, BOD2$MarketingFlags_content): Chi-squared
## approximation may be incorrect
chisq.test(BOD2$brand, BOD2$ingredients)
## Warning in chisq.test(BOD2$brand, BOD2$ingredients): Chi-squared approximation
## may be incorrect
## 
##  Pearson's Chi-squared test
## 
## data:  BOD2$brand and BOD2$ingredients
## X-squared = 104, df = 100, p-value = 0.3721
chisq.test(BOD2$brand, BOD2$category)
## Warning in chisq.test(BOD2$brand, BOD2$category): Chi-squared approximation may
## be incorrect
## 
##  Pearson's Chi-squared test
## 
## data:  BOD2$brand and BOD2$category
## X-squared = 9.7144, df = 8, p-value = 0.2856

H0: The variables are not associated i.e., are independent. (Null Hypothesis) H1: The variables are associated, i.e., are dependent. (Alternative Hypothesis)

If the “p” value is above 0.05, it means the probability of independence is fairly high and sufficient enough to conclude that the variables do not have a relationship. However, anything below 0.05 means that the probability of independence is insignificantly low, and the variables share a strong correlation.

chiqSB
## 
##  Pearson's Chi-squared test
## 
## data:  BOD2$brand and BOD2$MarketingFlags_content
## X-squared = 31.06, df = 12, p-value = 0.001929

The two variables in my data set that did have a strong correlation were Brand and Marketing Flags Content.

correlationSB <- table(BOD2$brand, BOD2$MarketingFlags_content, BOD2$name)

correlationSB
## , ,  = Alpha Beta® Exfoliating Moisturizer
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 1         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Alpha Beta® Pore Perfecting & Refining Serum
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 1         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Anti-Pollution Drops
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         1         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Brightening Face Cream
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         1         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Ceramidin™ Cream
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 1         0                       0           0
## 
## , ,  = Cicapair™ Tiger Grass Calming Gel Cream
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         1                       0           0
## 
## , ,  = Cicapair™ Tiger Grass Cream
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         1                       0           0
## 
## , ,  = Cicapair™ Tiger Grass Serum
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         1                       0           0
## 
## , ,  = Clarifying Face Cream
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         1         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Clarifying Spot Treatment
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         1         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Dark Spots No More® Triple Acid Spot Minimizing Concentrate
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         1                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Darker Skin Tones Face Cream
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         1         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Darker Skin Tones Hyaluronic Serum
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         1         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Do Not Age with Dr. Brandt Transforming Pearl Serum
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       1         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Face Cream Light
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         1         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Face Cream Rich
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         1         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Hyaluronic Marine Hydration Booster
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       1           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Lifesaver Skin Brightening Toner
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       1           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Night Serum
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           1
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Peptidin™ Firming Serum with Energy Peptides
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 1         0                       0           0
## 
## , ,  = Peptidin™ Radiance Serum with Energy Peptides
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 1         0                       0           0
## 
## , ,  = Stress Repair Face Cream with Niacinamide
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 1         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Stress Rescue Super Serum with Niacinamide
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 1         0                       0           0
##   Dr. Jart+                 0         0                       0           0
## 
## , ,  = Teatreement™ Moisturizer
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         1                       0           0
## 
## , ,  = Teatreement™ Toner
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       0           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         1                       0           0
## 
## , ,  = True Blue Hydrating Serum
## 
##                            
##                             0 exclusive exclusive · online only online only
##   Dr Roebuck's              0         0                       1           0
##   Dr. Barbara Sturm         0         0                       0           0
##   Dr. Brandt Skincare       0         0                       0           0
##   Dr. Dennis Gross Skincare 0         0                       0           0
##   Dr. Jart+                 0         0                       0           0

As we can see in this chart below Dr. Jart+ is a pretty popular brand.

BODplot <- ggplot(BOD, aes(x=rating, y=price, size = number_of_reviews, color=brand)) +
   geom_point(alpha=0.9)+
    scale_size(range = c(.1, 9), name="Customer Who Left a Review") +
  labs(title= "Battle of the Doctors")+
    ylab("Price (in USD)") +
    xlab("Ratings out of 5 Stars")

BODplot

BOD2bar <- barplot(table(BOD2$brand, BOD2$MarketingFlags_content),
                   main = "ChiSquare Test: Relationship Between Brand and Marketing Flag Content",
                   xlab = "Brand",
                   ylab = "Marketing Flags")

BOD3 <- sephora_website_dataset %>%
  select(brand, category, price, value_price, name) %>%
  filter(brand %in% c("Dr. Jart+")) %>%
  filter(category %in% c( "Face Serums")) %>%
  filter(price < 50) %>%
  filter(value_price < 50)

BOD3
## # A tibble: 8 x 5
##   brand     category    price value_price name                                  
##   <chr>     <chr>       <dbl>       <dbl> <chr>                                 
## 1 Dr. Jart+ Face Serums    46          46 Cicapair™ Tiger Grass Serum           
## 2 Dr. Jart+ Face Serums    18          18 Focuspot™ Micro Tip™ Patches          
## 3 Dr. Jart+ Face Serums    18          18 Focuspot™ Blemish Micro Tip™ Patch    
## 4 Dr. Jart+ Face Serums    48          48 Peptidin™ Radiance Serum with Energy ~
## 5 Dr. Jart+ Face Serums    18          18 Focuspot™ Dark Spot Micro Tip™ Patch  
## 6 Dr. Jart+ Face Serums    18          18 Focuspot™ Line & Wrinkle Micro Tip™ P~
## 7 Dr. Jart+ Face Serums    48          48 Peptidin™ Firming Serum with Energy P~
## 8 Dr. Jart+ Face Serums    18          18 Focuspot™ Dark Circle Micro Tip™ Patch
var.test(BOD3$value_price, BOD3$price) #As the p value is greater than 0.05, there is no evidence to suggest that the variances are unequal
## 
##  F test to compare two variances
## 
## data:  BOD3$value_price and BOD3$price
## F = 1, num df = 7, denom df = 7, p-value = 1
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.2002038 4.9949092
## sample estimates:
## ratio of variances 
##                  1
varttest3 <- t.test(BOD3$value_price, BOD3$price, var.equal = TRUE)

t.test(BOD3$value_price, BOD3$price)
## 
##  Welch Two Sample t-test
## 
## data:  BOD3$value_price and BOD3$price
## t = 0, df = 14, p-value = 1
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -16.29393  16.29393
## sample estimates:
## mean of x mean of y 
##        29        29
plot(x = BOD$value_price,y =BOD$price,
   xlab = "Value Price in USD",
   ylab = "Actual Price is USD",
   main = "Value Price vs Actual Price")