Avocado Pricing at Retail
Lizet Vazquez
3/01/2021
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Note: this analysis was performed using the open source software R and Rstudio.
Objective
The objective of this basic project is to explain the price of avocados using some basic descriptive analysis.This analysis can be used by producers, retailers, and groceries to make decisions about their pricing strategies, advertising strategies, and supply chain stratgies among others. Some additional analysis will follow after this episode. Your feedback is highly appreciated.
Dataset - weekly avocado sales and price data from the Hass Avocado Board website
This data was downloaded from the Hass Avocado Board website in May of 2018 & compiled into a single CSV. Here’s how the Hass Avocado Board describes the data on their website: The table below represents weekly retail scan data for National retail volume (units) and price. Retail scan data comes directly from retailers’ cash registers based on actual retail sales of Hass avocados. Starting in 2013, the table below reflects an expanded, multi-outlet retail data set. Multi-outlet reporting includes an aggregation of the following channels: grocery, mass, club, drug, dollar and military. The Average Price (of avocados) in the table reflects a per unit (per avocado) cost, even when multiple units (avocados) are sold in bags. The Product Lookup codes (PLU’s) in the table are only for Hass avocados. Other varieties of avocados (e.g. greenskins) are not included in this table.
data <- read.csv("avocado.csv")
head(data)## X Date AveragePrice Total_Volume X4046 X4225 X4770 Total.Bags
## 1 0 2015/12/27 1.33 64236.62 1036.74 54454.85 48.16 8696.87
## 2 1 2015/12/20 1.35 54876.98 674.28 44638.81 58.33 9505.56
## 3 2 2015/12/13 0.93 118220.22 794.70 109149.67 130.50 8145.35
## 4 3 2015/12/6 1.08 78992.15 1132.00 71976.41 72.58 5811.16
## 5 4 2015/11/29 1.28 51039.60 941.48 43838.39 75.78 6183.95
## 6 5 2015/11/22 1.26 55979.78 1184.27 48067.99 43.61 6683.91
## Small.Bags Large.Bags XLarge.Bags type year region
## 1 8603.62 93.25 0 conventional 2015 Albany
## 2 9408.07 97.49 0 conventional 2015 Albany
## 3 8042.21 103.14 0 conventional 2015 Albany
## 4 5677.40 133.76 0 conventional 2015 Albany
## 5 5986.26 197.69 0 conventional 2015 Albany
## 6 6556.47 127.44 0 conventional 2015 Albany#install.packages('plyr')
library(plyr)
count(data, 'region')## region freq
## 1 Albany 338
## 2 Atlanta 338
## 3 BaltimoreWashington 338
## 4 Boise 338
## 5 Boston 338
## 6 BuffaloRochester 338
## 7 California 338
## 8 Charlotte 338
## 9 Chicago 338
## 10 CincinnatiDayton 338
## 11 Columbus 338
## 12 DallasFtWorth 338
## 13 Denver 338
## 14 Detroit 338
## 15 GrandRapids 338
## 16 GreatLakes 338
## 17 HarrisburgScranton 338
## 18 HartfordSpringfield 338
## 19 Houston 338
## 20 Indianapolis 338
## 21 Jacksonville 338
## 22 LasVegas 338
## 23 LosAngeles 338
## 24 Louisville 338
## 25 MiamiFtLauderdale 338
## 26 Midsouth 338
## 27 Nashville 338
## 28 NewOrleansMobile 338
## 29 NewYork 338
## 30 Northeast 338
## 31 NorthernNewEngland 338
## 32 Orlando 338
## 33 Philadelphia 338
## 34 PhoenixTucson 338
## 35 Pittsburgh 338
## 36 Plains 338
## 37 Portland 338
## 38 RaleighGreensboro 338
## 39 RichmondNorfolk 338
## 40 Roanoke 338
## 41 Sacramento 338
## 42 SanDiego 338
## 43 SanFrancisco 338
## 44 Seattle 338
## 45 SouthCarolina 338
## 46 SouthCentral 338
## 47 Southeast 338
## 48 Spokane 338
## 49 StLouis 338
## 50 Syracuse 338
## 51 Tampa 338
## 52 TotalUS 338
## 53 West 338
## 54 WestTexNewMexico 335count(data, 'AveragePrice')## AveragePrice freq
## 1 0.44 1
## 2 0.46 1
## 3 0.48 1
## 4 0.49 2
## 5 0.51 5
## 6 0.52 3
## 7 0.53 6
## 8 0.54 7
## 9 0.55 3
## 10 0.56 12
## 11 0.57 9
## 12 0.58 14
## 13 0.59 5
## 14 0.60 12
## 15 0.61 11
## 16 0.62 10
## 17 0.63 10
## 18 0.64 17
## 19 0.65 23
## 20 0.66 10
## 21 0.67 23
## 22 0.68 26
## 23 0.69 18
## 24 0.70 44
## 25 0.71 28
## 26 0.72 30
## 27 0.73 38
## 28 0.74 50
## 29 0.75 43
## 30 0.76 61
## 31 0.77 65
## 32 0.78 53
## 33 0.79 67
## 34 0.80 60
## 35 0.81 60
## 36 0.82 66
## 37 0.83 81
## 38 0.84 64
## 39 0.85 79
## 40 0.86 73
## 41 0.87 77
## 42 0.88 88
## 43 0.89 98
## 44 0.90 94
## 45 0.91 92
## 46 0.92 101
## 47 0.93 141
## 48 0.94 123
## 49 0.95 127
## 50 0.96 143
## 51 0.97 147
## 52 0.98 189
## 53 0.99 185
## 54 1.00 167
## 55 1.01 159
## 56 1.02 160
## 57 1.03 179
## 58 1.04 174
## 59 1.05 178
## 60 1.06 170
## 61 1.07 168
## 62 1.08 194
## 63 1.09 167
## 64 1.10 161
## 65 1.11 169
## 66 1.12 158
## 67 1.13 192
## 68 1.14 180
## 69 1.15 202
## 70 1.16 168
## 71 1.17 174
## 72 1.18 199
## 73 1.19 188
## 74 1.20 155
## 75 1.21 151
## 76 1.22 167
## 77 1.23 181
## 78 1.24 165
## 79 1.25 170
## 80 1.26 193
## 81 1.27 155
## 82 1.28 147
## 83 1.29 149
## 84 1.30 140
## 85 1.31 139
## 86 1.32 137
## 87 1.33 159
## 88 1.34 164
## 89 1.35 163
## 90 1.36 187
## 91 1.37 159
## 92 1.38 155
## 93 1.39 148
## 94 1.40 175
## 95 1.41 167
## 96 1.42 149
## 97 1.43 185
## 98 1.44 172
## 99 1.45 157
## 100 1.46 150
## 101 1.47 160
## 102 1.48 185
## 103 1.49 180
## 104 1.50 170
## 105 1.51 148
## 106 1.52 161
## 107 1.53 160
## 108 1.54 173
## 109 1.55 163
## 110 1.56 151
## 111 1.57 134
## 112 1.58 146
## 113 1.59 186
## 114 1.60 159
## 115 1.61 125
## 116 1.62 139
## 117 1.63 136
## 118 1.64 133
## 119 1.65 123
## 120 1.66 141
## 121 1.67 129
## 122 1.68 138
## 123 1.69 127
## 124 1.70 115
## 125 1.71 85
## 126 1.72 117
## 127 1.73 96
## 128 1.74 106
## 129 1.75 105
## 130 1.76 115
## 131 1.77 85
## 132 1.78 97
## 133 1.79 112
## 134 1.80 116
## 135 1.81 119
## 136 1.82 125
## 137 1.83 115
## 138 1.84 88
## 139 1.85 102
## 140 1.86 90
## 141 1.87 84
## 142 1.88 94
## 143 1.89 80
## 144 1.90 83
## 145 1.91 73
## 146 1.92 81
## 147 1.93 79
## 148 1.94 63
## 149 1.95 59
## 150 1.96 59
## 151 1.97 54
## 152 1.98 50
## 153 1.99 49
## 154 2.00 59
## 155 2.01 59
## 156 2.02 54
## 157 2.03 39
## 158 2.04 42
## 159 2.05 38
## 160 2.06 59
## 161 2.07 48
## 162 2.08 38
## 163 2.09 47
## 164 2.10 26
## 165 2.11 37
## 166 2.12 26
## 167 2.13 35
## 168 2.14 26
## 169 2.15 33
## 170 2.16 30
## 171 2.17 29
## 172 2.18 32
## 173 2.19 26
## 174 2.20 21
## 175 2.21 22
## 176 2.22 20
## 177 2.23 19
## 178 2.24 22
## 179 2.25 22
## 180 2.26 15
## 181 2.27 20
## 182 2.28 13
## 183 2.29 16
## 184 2.30 20
## 185 2.31 24
## 186 2.32 20
## 187 2.33 24
## 188 2.34 19
## 189 2.35 14
## 190 2.36 18
## 191 2.37 18
## 192 2.38 13
## 193 2.39 14
## 194 2.40 13
## 195 2.41 7
## 196 2.42 6
## 197 2.43 10
## 198 2.44 10
## 199 2.45 8
## 200 2.46 7
## 201 2.47 4
## 202 2.48 8
## 203 2.49 5
## 204 2.50 6
## 205 2.51 6
## 206 2.52 4
## 207 2.53 2
## 208 2.54 9
## 209 2.55 9
## 210 2.56 5
## 211 2.57 10
## 212 2.58 9
## 213 2.59 10
## 214 2.60 2
## 215 2.61 6
## 216 2.62 8
## 217 2.63 2
## 218 2.64 5
## 219 2.65 8
## 220 2.66 3
## 221 2.67 7
## 222 2.68 1
## 223 2.69 2
## 224 2.70 3
## 225 2.71 4
## 226 2.72 3
## 227 2.73 8
## 228 2.74 3
## 229 2.75 3
## 230 2.76 5
## 231 2.77 3
## 232 2.78 1
## 233 2.79 4
## 234 2.80 2
## 235 2.81 3
## 236 2.82 3
## 237 2.83 6
## 238 2.84 4
## 239 2.85 4
## 240 2.86 4
## 241 2.87 3
## 242 2.88 3
## 243 2.89 3
## 244 2.90 1
## 245 2.91 1
## 246 2.92 2
## 247 2.93 4
## 248 2.94 2
## 249 2.95 1
## 250 2.96 1
## 251 2.97 1
## 252 2.99 2
## 253 3.00 2
## 254 3.03 1
## 255 3.04 1
## 256 3.05 1
## 257 3.12 1
## 258 3.17 1
## 259 3.25 1mean(data$AveragePrice)## [1] 1.405978median(data$AveragePrice)## [1] 1.37#Now let's find the mode of the variable "price." #mode(data$AveragePrice) does not work
#Let's find a built-in function instead
#See reference: https://stackoverflow.com/questions/2547402/is-there-a-built-in-function-for-finding-the-mode
freq <- tapply(data$AveragePrice,data$AveragePrice,length)
as.numeric(names(freq)[which.max(freq)])## [1] 1.15hist(data$AveragePrice,xlab="Average Price",main ="Frequency of Average Price")
# Let's try ggplot- should be more fun
# Histogram of average_price for conventional and organic avocados
library(ggplot2)
ggplot(data, aes(x = AveragePrice, fill = type)) + geom_histogram(bins = 30, col = "red") + scale_fill_manual(values = c("blue", "green")) + ggtitle("Frequency of Average Price - Oragnic vs. Conventional")
cor(data$Total_Volume,data$AveragePrice)## [1] -0.1927524Price elasticity
To calculate Price Elasticity of Demand we use the formula: PE = (ΔQ/ΔP) * (P/Q) (Iacobacci, 2015).
(ΔQ/ΔP) is determined by the coefficient in our regression analysis below. Here Beta represents the change in the dependent variable y with respect to x (i.e. Δy/Δx = (ΔQ/ΔP)). To determine (P/Q) we will use the average price and average sales volume (Salem, 2014).
plot(Total_Volume ~ AveragePrice, data)
regr <- lm(Total_Volume ~ AveragePrice, data)
abline(regr, col='red')
coefficients(regr)## (Intercept) AveragePrice
## 3174918 -1653136Beta <- regr$coefficients[["AveragePrice"]]
P <- mean(data$AveragePrice)
Q <- mean(data$Total_Volume)
elasticity <-Beta*P/Q
elasticity## [1] -2.732369Elasticity - What conclusions can you draw from the analysis?
How to interpret the value? I suggest that you check out the textbook and the reading, Salem, 2014 (see the link below). Are consumers willing to pay more for avocados? Why? Please check the textbook to find the criteria.
Ref: Salem, 2014. Price Elasticity with R. http://www.salemmarafi.com/code/price-elasticity-with-r/
365datascience. https://365datascience.com/trending/price-elasticity/
Forecasting
Smoothing average forecasting is usually explained as “A n-day simple moving avaerage (n-day SMA) is arithmetic average of prices of past n days.” See the formula available Ko (2020) Ko (2020). Techincal Analysis with R (second edition). ref: https://bookdown.org/kochiuyu/technical-analysis-with-r-second-edition/simple-moving-average-sma.html https://cran.r-project.org/web/packages/smooth/vignettes/sma.html
# Using Smoothing average forecasting
timeseries <- ts(data$AveragePrice)
plot.ts(timeseries)
library("forecast") # load the "forecast" R library## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zootimeseriesarima <- arima(timeseries, order=c(0,1,1)) # fit an ARIMA(0,1,1) model
# Use the function ets() to perform a forecasting model
fit <- ets(timeseries)
# Plot 20-year forecasts of the lynx series
fit %>% forecast(h = 200) %>% autoplot()
#We can plot the observed prices for the current periods, as well as the prices that would be predicted for the next 200 time periods.Conclusion - no predictive model is perfect (see the predicted negative values in prices)!!!
We can plot the observed prices for the current periods, as well as the prices that would be predicted for the next 200 time periods.
Please keep in mind that no predictive model is perfect and all models are probably wrong. That said, the predictive prices usually take positive values. However, in our case, we got some negative values. See the interpretation given by Coghlan, 2021 (Parasite Genomics Group, Wellcome Trust Sanger Institute, Cambridge, U.K.) https://a-little-book-of-r-for-time-series.readthedocs.io/en/latest/src/timeseries.html
“One worrying thing is that the model has predicted negative values for the volcanic dust veil index, but this variable can only have positive values! The reason is that the arima() and forecast.Arima() functions don’t know that the variable can only take positive values. Clearly, this is not a very desirable feature of our current predictive model.”
References:
Coghlan, 2021 (Parasite Genomics Group, Wellcome Trust Sanger Institute, Cambridge, U.K.). https://a-little-book-of-r-for-time-series.readthedocs.io/en/latest/src/timeseries.html
Forecasting using R. https://robjhyndman.com/eindhoven/2-1-StateSpace.pdf
Error, trend, seasonality - ets and its forecast model friends. http://freerangestats.info/blog/2016/11/27/ets-friends.