About

Qualitative Descriptive Analytics aims to gather an in-depth understanding of the underlying reasons and motivations for an event or observation. It is typically represented with visuals or charts.

Quantitative Descriptive Analytics focuses on investigating a phenomenon via statistical, mathematical, and computationaly techniques. It aims to quantify an event with metrics and numbers.

In this lab, we will explore both analytics using the data set provided.

Setup

Remember to always set your working directory to the source file location. Go to ‘Session’, scroll down to ‘Set Working Directory’, and click ‘To Source File Location’. Read carefully the below and follow the instructions to complete the tasks and answer any questions. Submit your work to RPubs as detailed in previous notes.

And now the fun begins :)

Task 1: Quantitative Analysis

Begin by reading in the data from the ‘marketing.csv’ file, and viewing it to make sure it is read in correctly.

mydata = read.csv(file="data/marketing.csv")
head(mydata)
##   case_number sales radio paper  tv pos
## 1           1 11125    65    89 250 1.3
## 2           2 16121    73    55 260 1.6
## 3           3 16440    74    58 270 1.7
## 4           4 16876    75    82 270 1.3
## 5           5 13965    69    75 255 1.5
## 6           6 14999    70    71 255 2.1

Now calculate the Range, Min, Max, Mean, STDEV, and Variance for each variable. Below is an example of how to compute the items for the variable ‘sales’.

Sales

#creating the variable "sales""
sales = mydata$sales

#Max Sales
MaxSales = max(sales)
MaxSales
## [1] 20450
#Min Sales
MinSales = min(sales)
MinSales
## [1] 11125
#Range
RangeSales = MaxSales-MinSales
RangeSales
## [1] 9325
#Mean
MeanSales = mean(sales)
MeanSales 
## [1] 16717.2
#Standard Deviation
SdSales = sd(sales)
SdSales
## [1] 2617.052
#Variance
VarSales = var(sales)
VarSales
## [1] 6848961
#Repeat the above calculations for radio, paper, tv, and pos (you need to create the variables radio, paper, tv, and pos; then you repeat the above calculations on each of these variables)
#creating the variable "sales"

An easy way to calculate all of these statistics of all of these variables is with the summary() function. Below is an example.

summary(mydata)
##   case_number        sales           radio           paper      
##  Min.   : 1.00   Min.   :11125   Min.   :65.00   Min.   :35.00  
##  1st Qu.: 5.75   1st Qu.:15175   1st Qu.:70.00   1st Qu.:53.75  
##  Median :10.50   Median :16658   Median :74.50   Median :62.50  
##  Mean   :10.50   Mean   :16717   Mean   :76.10   Mean   :62.30  
##  3rd Qu.:15.25   3rd Qu.:18874   3rd Qu.:81.75   3rd Qu.:75.50  
##  Max.   :20.00   Max.   :20450   Max.   :89.00   Max.   :89.00  
##        tv             pos       
##  Min.   :250.0   Min.   :0.000  
##  1st Qu.:255.0   1st Qu.:1.200  
##  Median :270.0   Median :1.500  
##  Mean   :266.6   Mean   :1.535  
##  3rd Qu.:276.2   3rd Qu.:1.800  
##  Max.   :280.0   Max.   :3.000
#Repeat the above for the variable "sales"" (i.e. use the summary() function on variable sales). 
#There are some statistics not calculated with the summary() function  Specify which.
summary(sales)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   11125   15175   16658   16717   18874   20450

Task 2: Qualitative Analysis

Now, we will produce a basic plot of the ‘sales’ variable . Here we utilize the plot function, and within the plot function we call the variable we want to plot.

#creating a plot for variable "sales"
plot(sales)

We can customize the plot by adding labels to the x- and y- axis.

#xlab labels the x axis, ylab labels the y axis
plot(sales, type="b", xlab = "Case Number", ylab = "Sales in $1,000")

There are further ways to customize plots, such as changing the colors of the lines, adding a heading, or even making them interactive.

Now, lets plot the sales graph, alongside radio, paper, and tv which you will code. Make sure to run the code in the same chunk so they are on the same layout.

#Function "Layout"" allows us to see all 4 graphs on one screen

layout(matrix(c(1,2,3,4),2,2))

# the above code allows us to divide the screen into 2 rows and 2 columns, and to include 4 graphs alongside each other in the divided screen. Below we write the codes for the 4 graphs / plots. I will write the first one, and you have to do the other 3 

#Example of how to plot the sales variable
plot(sales, type="b", xlab = "Case Number", ylab = "Sales in $1,000") 

#Plot of Radio. Label properly 
plot(sales, type="b", xlab = "Case Number", ylab = "Radio in $1,000") 

#Plot of Paper. Label properly
plot(sales, type="b", xlab = "Case Number", ylab = "Paper in $1,000") 

#Plot of TV. Label properly
plot(sales, type="b", xlab = "Case Number", ylab = "TV in $1,000")

When looking at these plots it is hard to see a particular trend. One way to observe any possible trend in the sales data would be to re-order the data from low to high. The 20 months case studies are in no particular chronological time sequence. The 20 case numbers are independent sequentially generated numbers. Since each case is independent, we can reorder them.

#Re-order sales from low to high, and save re-ordered data in a new set. As sales data is re-reorded associated other column fields follow.
newdata = mydata[order(sales),]
head(newdata)
##    case_number sales radio paper  tv pos
## 1            1 11125    65    89 250 1.3
## 19          19 12369    65    37 250 2.5
## 20          20 13882    68    80 252 1.4
## 5            5 13965    69    75 255 1.5
## 6            6 14999    70    71 255 2.1
## 11          11 15234    70    66 255 1.5
# Redefining the variables to capture the new ordering  
newsales = newdata$sales
newradio = newdata$radio
newtv = newdata$tv
newpaper = newdata$paper
#Repeat the 4 graphs layout with proper labeling using instead the four new variables for sales, radio, tv, and paper. 
# you have to first include the function "layout"" as we did above
# then you have to plot newsales, newradio, newtv, and newpaper

#Example of how to plot the sales variable
plot(newsales, type="b", xlab = "Case Number", ylab = "newsales in $1,000") 

#Plot of Radio. Label properly 
plot(newsales, type="b", xlab = "Case Number", ylab = "newRadio in $1,000") 

#Plot of Paper. Label properly
plot(newsales, type="b", xlab = "Case Number", ylab = "newPaper in $1,000") 

#Plot of TV. Label properly
plot(newsales, type="b", xlab = "Case Number", ylab = "newtv in $1,000")

Shares your observations on what the new plots are revealing in terms of trending relationship. The new plots are revealing an upward trending curve. ———-

Task 3: Standarized Z-Value

Given a sales value of $25000, calculate the corresponding z-value or z-score using the mean and standard deviation calculations conducted in task 1. We know that z-score = (x - mean)/sd.

#  Show calculations here
(25000-mean(sales))/sd(sales)
## [1] 3.164935

Based on the z-value, how would you rate a $25000 sales value: poor, average, good, or very good performance? Explain your logic.

Z-score value is 3.16. This is a poor value because a score beyond 3 is a ddefinite outlier.