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.

Radio

radio = mydata$radio
#Max Radio
max = max(radio)
max 
## [1] 89
#Min Radio 
min = min(radio)
min
## [1] 65
#Range 
max-min
## [1] 24
#Mean 
mean(radio)
## [1] 76.1
#Standard Deviation 
sd(radio)
## [1] 7.354912
#Variance
var(radio)
## [1] 54.09474

Paper

paper = mydata$paper 
#Max Paper 
max = max(paper)
max
## [1] 89
#Min Paper
min = min(paper)
min 
## [1] 35
#Range
max-min
## [1] 54
#Mean
mean(paper)
## [1] 62.3
#Standard Deviation 
sd(paper)
## [1] 15.35921
#Variance
var(paper)
## [1] 235.9053

Tv

tv = mydata$tv
#Max Tv
max = max(tv) 
max 
## [1] 280
#Min  Tv 
min = min(tv)
min
## [1] 250
#Range 
max-min
## [1] 30
#Mean 
mean(tv)
## [1] 266.6
#Standard Deviation 
sd(tv)
## [1] 11.3388
#Variance
var(tv)
## [1] 128.5684

Pos

pos = mydata$pos
#Max Pos 
max = max(pos)
max 
## [1] 3
#Min Pos
min = min(pos)
min 
## [1] 0
#Range 
max-min
## [1] 3
#Mean
mean(pos)
## [1] 1.535
#Standard Deviation 
sd(pos)
## [1] 0.7499298
#Variance 
var(pos)
## [1] 0.5623947
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 varialble sales. There are some statistics not calculated with the summary() function Specify which.

The statistics not calculated are range, standard deviation, and variance.

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 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")

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

#Plot of TV. Label properly
plot(tv, type="b", xlab = "Case Number", ylab = "TV")

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.

layout(matrix(1:4,2,2))
plot(newsales, type="b", xlab = "Case Number", ylab = "Sales in $1,000")
plot(newradio, type="b", xlab = "Case Number", ylab = "Radio")
plot(newpaper, type="b", xlab = "Case Number", ylab = "Paper")
plot(newtv, type="b", xlab = "Case Number", ylab = "TV")

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

The new plots reveal that radio and Tv both have a positive correlation with sales, meaning that as radio and tv promotions go up, sales tend to go up as well. Paper does not have a clear correlation with sales, which means that the amount of money spent on paper-form marketing does not have a significant impact on sales. There may be other variables affecting the paper-form related data. Based on this data alone, it would be wise to spend money on radio and Tv marketing based on the positive correlation.

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.

x=25000
zscore = (x-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.

The mean for the sales data is $16712.2. The z score shows the number of standard deviations $25000 is from the mean. A z score of 3.16 shows that the figure is a little more than three standard deviations away from means sales. Poor performance would be if sales were lower than the mean, average could be one standard deviation away from the mean at most, and good might be around two standard deviations. A z score greater than three is an outlier, which is where $25000 is. Since higher sales are the goal, an outlier greater than the mean, in terms of sales, indicates very good performance.