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Introduction

It is tough to make good predictions. The numerous factors or variables, independent and dependent, involved in many sporting events contribute to the unpredictability. However, using carefully-selected variables, it is still possible to make marketing promotions more accountable.

The goal of this case study is to analyze if bobblehead promotions increase attendance at Dodgers home games. Using the fitted predictive model we can predict the attendance for the game in the forthcoming season and we can predict the attendance with or without bobblehead promotion.

The motivation of this case study is to design a predictive model, and report any interesting findings to support critical business decision making.

Pre-Processing

Important Tips: please make sure to reset your working directory before performing the analysis.

Load the required libraries and the data

#rm(list=ls())# clear memory

#setwd("C:/Users/zxu3/Documents/R/regression") 

library(lattice) # Graphics Package
library(ggplot2) # Graphical Package

#Create a dataframe with the Dodgers Data  - if you import the data from your own drive
#DodgersData <- read.csv("DodgersData.csv")

 

 

library(readr)

#adding a hashtag to the beginning of a line of syntax allows you to take notes or add descriptions.

#Now upload the following dataset to your work environment. 

DodgersData <- read_csv("DodgersData.csv")
## Rows: 81 Columns: 12
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (9): month, day_of_week, opponent, skies, day_night, cap, shirt, firewor...
## dbl (3): day, attend, temp
## 
## 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.
#Alternatively, you can read the data from my Github website.

Data cleanup and exploratory analysis

Evaluate the Structure and Re-Level the factor variables for “Day Of Week”” and “Month”” in the right order

# Check the structure for Dorder Data
str(DodgersData)
## spc_tbl_ [81 × 12] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ month      : chr [1:81] "APR" "APR" "APR" "APR" ...
##  $ day        : num [1:81] 10 11 12 13 14 15 23 24 25 27 ...
##  $ attend     : num [1:81] 56000 29729 28328 31601 46549 ...
##  $ day_of_week: chr [1:81] "Tuesday" "Wednesday" "Thursday" "Friday" ...
##  $ opponent   : chr [1:81] "Pirates" "Pirates" "Pirates" "Padres" ...
##  $ temp       : num [1:81] 67 58 57 54 57 65 60 63 64 66 ...
##  $ skies      : chr [1:81] "Clear" "Cloudy" "Cloudy" "Cloudy" ...
##  $ day_night  : chr [1:81] "Day" "Night" "Night" "Night" ...
##  $ cap        : chr [1:81] "NO" "NO" "NO" "NO" ...
##  $ shirt      : chr [1:81] "NO" "NO" "NO" "NO" ...
##  $ fireworks  : chr [1:81] "NO" "NO" "NO" "YES" ...
##  $ bobblehead : chr [1:81] "NO" "NO" "NO" "NO" ...
##  - attr(*, "spec")=
##   .. cols(
##   ..   month = col_character(),
##   ..   day = col_double(),
##   ..   attend = col_double(),
##   ..   day_of_week = col_character(),
##   ..   opponent = col_character(),
##   ..   temp = col_double(),
##   ..   skies = col_character(),
##   ..   day_night = col_character(),
##   ..   cap = col_character(),
##   ..   shirt = col_character(),
##   ..   fireworks = col_character(),
##   ..   bobblehead = col_character()
##   .. )
##  - attr(*, "problems")=<externalptr>
head(DodgersData)
## # A tibble: 6 × 12
##   month   day attend day_of_week opponent  temp skies  day_night cap   shirt
##   <chr> <dbl>  <dbl> <chr>       <chr>    <dbl> <chr>  <chr>     <chr> <chr>
## 1 APR      10  56000 Tuesday     Pirates     67 Clear  Day       NO    NO   
## 2 APR      11  29729 Wednesday   Pirates     58 Cloudy Night     NO    NO   
## 3 APR      12  28328 Thursday    Pirates     57 Cloudy Night     NO    NO   
## 4 APR      13  31601 Friday      Padres      54 Cloudy Night     NO    NO   
## 5 APR      14  46549 Saturday    Padres      57 Cloudy Night     NO    NO   
## 6 APR      15  38359 Sunday      Padres      65 Clear  Day       NO    NO   
## # ℹ 2 more variables: fireworks <chr>, bobblehead <chr>
# Evaluate the factor levels for day_of_week
# levels(DodgersData$day_of_week)

 

# Evaluate the factor levels for month
levels(DodgersData$month)
## NULL
# First 10 rows of the data frame
head(DodgersData, 10)
## # A tibble: 10 × 12
##    month   day attend day_of_week opponent   temp skies  day_night cap   shirt
##    <chr> <dbl>  <dbl> <chr>       <chr>     <dbl> <chr>  <chr>     <chr> <chr>
##  1 APR      10  56000 Tuesday     Pirates      67 Clear  Day       NO    NO   
##  2 APR      11  29729 Wednesday   Pirates      58 Cloudy Night     NO    NO   
##  3 APR      12  28328 Thursday    Pirates      57 Cloudy Night     NO    NO   
##  4 APR      13  31601 Friday      Padres       54 Cloudy Night     NO    NO   
##  5 APR      14  46549 Saturday    Padres       57 Cloudy Night     NO    NO   
##  6 APR      15  38359 Sunday      Padres       65 Clear  Day       NO    NO   
##  7 APR      23  26376 Monday      Braves       60 Cloudy Night     NO    NO   
##  8 APR      24  44014 Tuesday     Braves       63 Cloudy Night     NO    NO   
##  9 APR      25  26345 Wednesday   Braves       64 Cloudy Night     NO    NO   
## 10 APR      27  44807 Friday      Nationals    66 Clear  Night     NO    NO   
## # ℹ 2 more variables: fireworks <chr>, bobblehead <chr>

Let R identify the temperature, the attendance, the opponent, and the promotion (i.e., bobblehead) for the 20th home game of the season.

DodgersData[20, c("temp", "attend", "opponent", "bobblehead")]
## # A tibble: 1 × 4
##    temp attend opponent bobblehead
##   <dbl>  <dbl> <chr>    <chr>     
## 1    70  47077 Snakes   YES

Let R identify the average value for attendance.

meanattend <- mean(DodgersData$attend)
meanattend
## [1] 41040.07

Let R identify the number of promotions they have had.

promotions <- sum(DodgersData$bobblehead=="YES")
promotions
## [1] 11
## in-class notes

Note: You may perform the regression analysis using Excel.

If you chose to use R and RStudio, please work on any two of the first three questions (1a, 1b, and 1c) and the last two questions (2 and 3).

If you chose to use Excel, please post your spreadsheet solutions and the answers to Questions 1a, 1b, 1c, 2, and 3.

Q 1a: Let R identify the temperature, the attendance, the opponent, and the promotion (i.e., bobblehead) for the 25th home game of the season. Report your results.

Answer:

Q 1b: What is the median value of attendance? Please review your in-class notes and write your function and answer below.

medianattend <- median(DodgersData$attend)
medianattend

Q 1c: How many night games did the Dodgers have? Please review your in-class notes and write your function and answer below.

night_games<- sum(DosdgersData$day_night=="Night")
night_games

Answer:

Q 2: Interpret one of the box plots or scatter plots in plain language.

Answer: I will interpret the scatter plot titled “Dodgers Attendance By Temperature By Time of Game and Skies”. When looking at the scatter plots on clear and cloudy days during the day there aren’t fireworks, but during the night there is a bigger possibility of fireworks on clear nights compared to cloudy nights.I do think that the number of attendance and temperature doesn’t correlate to when there would be fireworks.

Q 3: Explain the final statistical results in plain language.

Answer:The final statistical results at the end of this title “Design Predictive Model” shows several data such as the estimate of attendance based on month, day of the week and bobble heads.The 5 number summary as shown on the top it shows the min, median and max and well as Q1 and Q3. The minimum being -10786.5 and the maximum being 14351. After that it’s shows the months and also the days of the week with the estimate which gives a good estimate on what months or what day during the week more people attend the game.

Q 4: Please read the tutorial “Advanced topics - Formatting a testable marketing hypothesis.docx” and develop two “draft” hypotheses for your group project.

Answer:

Exploratory analysis

The results show that in 2012 there were a few promotions (see the last four columns)

Cap Shirt Fireworks Bobblehead

We have data from April to October for games played in the Day or Night under Clear or Cloudy Skys.

Dodger Stadium has a capacity of about 56,000. Looking at the entire (sample) data shows that the stadium filled up only twice in 2012. There were only two cap promotions, three shirt promotions - not enough data for any inferences. Fireworks and Bobblehead promotions have happened a few times.

Further more there were eleven bobble head promotions and most of then (six) being on Tuesday nights.

Evaluate Attendance by Weather

#Evaluate attendance by weather
ggplot(DodgersData, aes(x=temp, y=attend/1000, color=fireworks)) +
geom_point() +
facet_wrap(day_night~skies) +
ggtitle("Dodgers Attendance By Temperature By Time of Game and Skies") +
theme(plot.title = element_text(lineheight=3, face="bold", color="black", size=10)) +
xlab("Temperature (Degree Farenheit)") +
ylab("Attendance (Thousands)")

Strip Plot of Attendance by opponent or visiting team

#Strip Plot of Attendance by opponent or visiting team
ggplot(DodgersData, aes(x=attend/1000, y=opponent, color=day_night)) +
geom_point() +
ggtitle("Dodgers Attendance By Opponent") +
theme(plot.title = element_text(lineheight=3, face="bold", color="black", size=10)) +
xlab("Attendance (Thousands)") +
ylab("Opponent (Visiting Team)")

##Design Predictive Model

To advise the management if promotions impact attendance we will need to identify if there is a positive effect, and if there is a positive effect how much of an effect it is.

To provide this advice, I built a Linear Model for predicting attendance using Month, Day Of Week and the indicator variable Bobblehead promotion. I split the data into Training and Test to create the model

# Create a model with the bobblehead variable entered last
my.model <- {attend ~ month + day_of_week + bobblehead}

# use the full data set to obtain an estimate of the increase in
# attendance due to bobbleheads, controlling for other factors
my.model.fit <- lm(my.model, data = DodgersData) # use all available data
print(summary(my.model.fit))
## 
## Call:
## lm(formula = my.model, data = DodgersData)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10786.5  -3628.1   -516.1   2230.2  14351.0 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          38792.98    2364.68  16.405  < 2e-16 ***
## monthAUG              2377.92    2402.91   0.990   0.3259    
## monthJUL              2849.83    2578.60   1.105   0.2730    
## monthJUN              7163.23    2732.72   2.621   0.0108 *  
## monthMAY             -2385.62    2291.22  -1.041   0.3015    
## monthOCT              -662.67    4046.45  -0.164   0.8704    
## monthSEP                29.03    2521.25   0.012   0.9908    
## day_of_weekMonday    -4883.82    2504.65  -1.950   0.0554 .  
## day_of_weekSaturday   1488.24    2442.68   0.609   0.5444    
## day_of_weekSunday     1840.18    2426.79   0.758   0.4509    
## day_of_weekThursday  -4108.45    3381.22  -1.215   0.2286    
## day_of_weekTuesday    3027.68    2686.43   1.127   0.2638    
## day_of_weekWednesday -2423.80    2485.46  -0.975   0.3330    
## bobbleheadYES        10714.90    2419.52   4.429 3.59e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6120 on 67 degrees of freedom
## Multiple R-squared:  0.5444, Adjusted R-squared:  0.456 
## F-statistic: 6.158 on 13 and 67 DF,  p-value: 2.083e-07