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.

Note

For your assignment you may be using different data sets than what is included here. Read carefully the instructions on Sakai.

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

sales = mydata$sales
#Max Sales
max = max(sales)
max
## [1] 20450
#Min Sales
min = min(sales)
min
## [1] 11125
#Range
max-min
## [1] 9325
#Mean
mean(sales)
## [1] 16717.2
#Standard Deviation
sd(sales)
## [1] 2617.052
#Variance
var(sales)
## [1] 6848961
#Repeat the above calculations for radio, paper, tv, and pos. 
#paper
paper =mydata$paper
max = max(paper)
max
## [1] 89
min=min(paper)
min
## [1] 35
max-min
## [1] 54
mean(paper)
## [1] 62.3
sd(paper)
## [1] 15.35921
var(paper)
## [1] 235.9053
radio =mydata$radio
max = max(radio)
max
## [1] 89
min = min(radio)
min
## [1] 65
max-min
## [1] 24
mean(radio)
## [1] 76.1
sd(radio)
## [1] 7.354912
var(radio)
## [1] 54.09474
tv =mydata$tv
max = max(tv)
max
## [1] 280
min= min(tv)
min
## [1] 250
max-min
## [1] 30
mean(tv)
## [1] 266.6
sd(tv)
## [1] 11.3388
var(tv)
## [1] 128.5684
pos =mydata$pos
max = max(pos)
max
## [1] 3
min = min(pos)
min
## [1] 0
max-min
## [1] 3
mean(pos)
## [1] 1.535
sd(pos)
## [1] 0.7499298
var(pos)
## [1] 0.5623947

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
summary(mydata$sales)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   11125   15175   16658   16717   18874   20450
#Repeat the above for the varialble sales. There are some statistics not calculated with the summary() function  Specify which.

Task 2: Qualitative Analysis

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

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.

#Layout allows us to see all 4 graphs on one screen
layout(matrix(1:4,2,2))

#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(radio, type="b", xlab = "Case Number", ylab = "Radio in $1,000")

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

#Plot of TV. Label properly
plot(tv, 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
# Redefine the new variables 
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. 
plot(newdata$sales, type="b", xlab = "Case Number", ylab = "Sales in $1,000") 

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

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

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

Shares your observations on what the new plots are revealing in terms of trending relationship.

Conclusions can be made by comparing the sales graph to the subsequent 3. We see that there is a direct relationship between increased marketing through radio and tv. Although, if one were to compare the paper graph and the sales graph, an inverse relationship would be discovered, thus suggesting paper marketing should be eliminated.

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
# z-score = (x-mean)/sd

# Sales
sales =newdata$sales
mean(sales)
## [1] 16717.2
sd(sales)
## [1] 2617.052
zscore=(25000-mean(sales))/sd(sales)
zscore
## [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.

Based on the Z-value of sales (3.165), a ‘$25,000’ sales value could be rated as very good performance. The z-value represents how many standard deviations away from the mean the value is. Thus, with the Standard Deviation of Sales being ‘$2,617.05’, this would mean the ‘$25,000’ value is ‘$8,282.80’ away from the mean sales value. To test this relationship, if one were to subrtract 3.16 standard deviations from ‘$25,000’, they would receive the mean sales value, ’$16,717.02. While this does provide valuable information on their performance, a more interesting bit of information would be, “How did we attain a sales value this high?”.