I'm dealing with some math problems here. We have the average sale and loss number in 3 stores.
Site SALE LOSS % LOSS
-------------------------------------------
Store 1 474750 336740 70,92996314 (LOSS*100)/SALE
Store 2 321920 247810 76,97875249
Store 3 149240 118440 79,36210131
-------------------------------------------
Total 945910 702990 74,31890983
If i sum the loss percentages of store 1,2 and 3 i get an average of 75.75.
But when i calculate the total SALE and LOSS and calculate the percentage LOSS i get 74.31?
Shouldent the numbers match? Or is this the wrong way?
Thank you for all answers!
You can't average percentages when they're taken from different totals. Calculating the total sale and loss is the correct way to do the calculation.
See Averaging Percentages on the Ask Dr. Math forum.
It would be the same only if the Sales are equal on the 3 stores.
In general:
(A+B+C)/(D+E+F) != (A/D+B/E+C/F)/3
But imagine equal sales D=E=F
(A+B+C)/(D+E+F) = (A+B+C)/(3D)
(A/D+B/E+C/F)/3 = (A/D+B/D+C/D)/3 = (A+B+C)/(3D)
Related
I've got a dataset that has monthly metrics for different stores. Each store has three monthly (Total sales, customers and transaction count), my task is over a year I need to find the store that most closely matches a specific test store (Ex: Store 77).
Therefore over the year both the test store and most similar store need to have similar performance. My question is how do I go about finding the most similar store? I've currently used euclidean distance but would like to know if there's a better way to go about it.
Thanks in advance
STORE
month
Metric 1
22
Jan-18
10
23
Jan-18
20
Is correlation a better way to measure similarity in this case compared to distance? I'm fairly new to data so if there's any resources where I can learn more about this stuff it would be much appreciated!!
In general, deciding similarity of items is domain-specific, i.e. it depends on the problem you try to solve. Therefore, there is not one-size-fits-all solution. Nevertheless, there is some a basic procedure someone can follow trying to solve this kind of problems.
Case 1 - only distance matters:
If you want to find the most similar items (stores in our case) using a distance measure, it's a good tactic to firstly scale your features in some way.
Example (min-max normalization):
Store
Month
Total sales
Total sales (normalized)
1
Jan-18
50
0.64
2
Jan-18
40
0.45
3
Jan-18
70
0
4
Jan-18
15
1
After you apply normalization on all attributes, you can calculate euclidean distance or any other metric that you think it fits your data.
Some resources:
Similarity measures
Feature scaling
Case 2 - Trend matters:
Now, say that you want to find the similarity over the whole year. If the definition of similarity for your problem is just the instance of the stores at the end of the year, then distance will do the job.
But if you want to find similar trends of increase/decrease of the attributes of two stores, then distance measures conceal this information. You would have to use correlation metrics or any other more sophisticated technique than just a distance.
Simple example:
To keep it simple, let's say we are interested in 3-months analysis and that we use only sales attribute (unscaled):
Store
Month
Total sales
1
Jan-18
20
1
Feb-18
20
1
Mar-18
20
2
Jan-18
5
2
Feb-18
15
2
Mar-18
40
3
Jan-18
10
3
Feb-18
30
3
Mar-18
78
At the end of March, in terms of distance Store 1 and Store 2 are identical, both having 60 total sales.
But, as far as the increase ratio per month is concerned, Store 2 and Store 3 is our match. In February they both had 2 times more sales and in March 1.67 and 1.6 times more sales respectively.
Bottom line: It really depends on what you want to quantify.
Well-known correlation metrics:
Pearson correlation coefficient
Spearman correlation coefficient
I am trying to use MatchIt to perform Propensity Score Matching (PSM) for my panel data. The data is panel data that contains multi-year observations from the same group of companies.
The data is basically describing a list of bond data and the financial data of their issuers, also the bond terms such as issued date, coupon rate, maturity, and bond type of bonds issued by them. For instance:
Firmnames
Year
ROA
Bond_type
AAPL US Equity
2015
0.3
0
AAPL US Equity
2015
0.3
1
AAPL US Equity
2016
0.3
0
AAPL US Equity
2017
0.3
0
C US Equity
2015
0.3
0
C US Equity
2016
0.3
0
C US Equity
2017
0.3
0
......
I've already known how to match the observations by the criteria I want and I use exact = Year to make sure I match observations from the same year. The problem now I am facing is that the observations from the same companies will be matched together, this is not what I want. The code I used:
matchit(Bond_type ~ Year + Amount_Issued + Cpn + Total_Assets_bf + AssetsEquityRatio_bf + Asset_Turnover_bf, data = rdata, method = "nearest", distance = "glm", exact = "Year")
However, as you can see, in the second raw of my sample, there might be two observations in one year from the same companies due to the nature of my study (the company can issue bonds more than one time a year). The only difference between them is the Bond_type. Therefore, the MathcIt function will, of course, treat them as the best control and treatment group and match these two observations together since they have the same ROA and other matching factors in that year.
I have two ways to solve this in my opinion:
Remove the observations from the same year and company, however, removing the observations might lead to bias results and ruined the study.
Preventing MatchIt function match the observations from the same company (or with the same Frimnames)
The second approach will be better since it will not lead to bias, however, I don't know if I can do this in MatchIt function. Hope someone can give me some advice on this or maybe there's any better solution to this problem, please be so kind to share with me, thanks in advance!
Note: If there's any further information or requirement I should provide, please just inform me. This is my first time raising the question here!
This is not possible with MatchIt at the moment (though it's an interesting idea and not hard to implement, so I may add it as a feature).
In the optmatch package, which perfroms optimal pair and full matching, there is a constraint that can be added called "anti-exact matching", which sounds exactly like what you want. Units with the same value of the anti-exact matching variable will not be matched with each other. This can be implemented using optmatch::antiExactMatch().
In the Matching package, which performs nearest neighbor and genetic matching, the restrict argument can be supplied to the matching function to restrict certain matches. You could manually create the restriction matrix by restricting all pairs of observations in the same company and then supply the matrix to Match().
I am currently working on the so-called "Moneyball" problem. I am basically trying to select the best combination of three baseball players (based on certain baseball-relevant statistics) for the least amount of money.
I have the following dataset (OBP, SLG, and AB are statistics that describe the performance of a player):
# the table has about 100 observations;
# the data frame is called "batting.2001"
playerID OBP SLG AB salary
giambja01 0.3569001 0.6096154 20 410333
heltoto01 0.4316547 0.4948382 57 4950000
berkmla01 0.2102326 0.6204506 277 305000
gonzalu01 0.4285714 0.3880131 409 9200000
martied01 0.4234079 0.5425532 100 5500000
My goal is to pick three players who in combination have the highest possible sum of OBP, SLG, and AB, but at the same time do not exceed a total salary of 15.000.000 dollar.
My approach so far has been rather simple... I just tried to arrange (in descending order) the columns OBP, SLG, and AB and simply picking the three players on the top that in combination do not exceed the salary restriction of 15 Million dollar:
batting.2001 %>%
arrange(desc(OPB), desc(SLG), desc(AB))
Can anyone of you think of a better solution? Also, what if I would like to get the best combination of three players for the least amount of money? What approach would you use in that scenario?
Thanks in advance, and looking forward to reading your solutions.
Hello and thank you for looking at this question.
I have three columns: User ID, Status (active or inactive) and Tenure (target or no). I want to sample 428 of these ID's 100 times (with replacement). The samples must be 77% target tenure and 23% no tenure. The end goal is to see the average percentage of active and inactive ID's for the 100 samples. I'm using R for this analysis and I'm pretty new, so far I can only get the random sampling
sample <- data[sample(1:nrow(data),428,replace = TRUE),]
Any help or ideas would be incredible, thanks so much
I am trying to generate appointment times for yearly scheduled visits. The available days=1:365 and the first appointment should be randomly chosen first=sample(days,1,replace=F)
Now given the first appointment I want to generate 3 more appointment in the space between 1:365 so that there will be exactly 4 appointments in the 1:365 space, and as equally spaced between them as possible.
I have tried
point<-sort(c(first-1:5*364/4,first+1:5*364/4 ));point<-point[point>0 & point<365]
but it does not always give me 4 appointments. I have eventually run this many times and picked only the samples with 4 appointments, but I wanted to ask if there is a more elegant way to get exactly 4 points as equally distanced a s possible.
I was thinking of equal spacing (around 91 days between appointments) in a year starting at the first appointment... Essentially one appointment per quarter of the year.
# Find how many days in a quarter of the year
quarter = floor(365/4)
first = sample(days, 1)
all = c(first, first + (1:3)*quarter)
all[all > 365] = all[all > 365] - 365
all
sort(all)
Is this what you're looking for?
set.seed(1) # for reproducible example ONLY - you need to take this out.
first <- sample(1:365,1)
points <- c(first+(0:3)*(365-first)/4)
points
# [1] 97 164 231 298
Another way uses
points <- c(first+(0:3)*(365-first)/3)
This creates 4 points euqally spaced on [first, 365], but the last point will always be 365.
The reason your code is giving unexpected results is because you use first-1:5*364/4. This creates points prior to first, some of which can be < 0. Then you exclude those with points[points>0...].