# Regression, Time Shifted?

Six Sigma – iSixSigma Forums General Forums General Regression, Time Shifted?

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• #53977

Jeff Marth
Participant

Problem: Trying to determine if Input A has a time delayed, immediate, or any impact to Output B.

Scenario: Evaluating some items with our staffing policies. If the staff work a full day of overtime, they can choose to get the overtime pay or have a paid day off within the same month. What we can’t always tell is if allowing that paid day off is actually driving more OT than what we are willing to accept. The problem is that it may not drive additional overtime on the same day. The delay of impact could be as long as five days out.

How can I test for this in Minitab? If I knew the time delay I would just manually shift the data.

Suggestions?! Thank you!

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#192405

MBBinWI
Participant

@jpmarth – before trying to test for something in Minitab, I think you need to formulate a better question. Try looking at a different time period for your baseline. What is the maximum time period over which the overtime may be paid or taken as time off. Since the time off will require backfill, your baseline must include that time period in the analysis.

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#192409

Jeff Marth
Participant

The time period available is for all of 2011 up to the current. And since they must take the day off within the same month, this provides a limit to how far out the impact could be.

The data is not the problem. I have all the data I need to run the analysis and what I need answered. The problem is HOW to run this properly.

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#192411

Robert Butler
Participant

MBBinWI isn’t questioning the data nor the availability rather he is questioning the formulation of the question itself. My understanding of your initial post is as follows:

1. A person works a full day of overtime.
a. They can choose to get overtime pay which is greater than regular pay – but no time off
b. They can choose regular pay and a day off.
1. If they choose to have a day off they can take that day any time up to one month after the day they worked overtime.

If this is an accurate summation of your situation then it sounds like the question you are asking and trying to answer is this:

When people take a day off does their absence result in a need for more overtime on the part of other people in the work force?

If that is the question you are trying to answer then it seems like you would want to compare overtime hours worked on days when no one is absent because they chose to take option “b” vs. overtime hours worked on days when one or more people are absent because they did choose option “b” for that particular day.

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#192445

Paulonis
Participant

I think Robert Butler has the right kind of idea as to what analysis will give the desired answer.

However, in general, if you are trying to find a time shift between input and output, performing a cross-correlation analysis may be appropriate. Cross-correlation will tell you the linear correlation coefficient between input and output for a range of lags between the input and output. In Minitab, go to Stat/Time Series/Cross Correlation. You can use the Help button on the dialog box to get more information. With the optimal lag, you can then manually shift the data series and perform typical regression.

In this case, I don’t think cross-correlation is going to get you what you are looking for. Because the day off can be taken any time in the same month you are going to get a lot of smearing of any effect over many possible time lags. The result is that none are likely to be significant, even if there is a significant effect. Robert’s approach is more likely to give you the answer you need.

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#192450

Ronald Barr
Participant

Perhaps there is a different way to look at this….what if you looked at the correlation between staffing levels (available labor) and overtime. The amount of overtime might be independent of when time off is given because of time shifting (which is the problem that you are trying to solve). Another possible noise factor would be sick time, vacation time etc. The overtime hours should be independent of the reason why the time is taken off, and instead should correlate to labor hours available with perhaps a time shift to labor hours actually worked.

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#192471

Joan Ambrose
Guest

Another way to approach this is very simply from a logic point of view. If I understand your question correctly, Jeff, a person EITHER gets paid overtime for an extra day of work, OR gets a day off, and there is no pay involved if they choose to take a day off/comp day. Is that how the policy works?

IF thats how your policy works, then when a person chooses to be paid for the day, you pay one day of overtime pay, period. But, if that person chooses to take a day off, there is zero pay for that person. There may or may not be overtime paid to another employee, depending on whether you have to provide coverage for the day off taken by the first employee. Then, the employee providing coverage could choose to either get paid overtime or take a day off, and so it continues. If you think this through (drawing a quick flowchart is helpful) the direct result is that you only ever pay overtime to one person, either the first person who worked overtime, or the person who covered for them while they took a day off, or to the person who covered for the person who covered for the first person who worked overtime, etc.

The logic shows that only one person, at most, gets paid overtime for a day of overtime worked. No one gets additional pay if the day off taken does not require coverage, so the policy may be saving you money. And, since people like choice, it may also be making for happier employees.

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#192472

Joan Ambrose
Participant

Ack! And, now that I see my error, how do I edit that post?

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#192474

MBBinWI
Participant

@joanambrose – go back and edit it (click on the message number in the upper right corner above the post).

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#192475

Joan Ambrose
Participant

It won’t let me. I think I was inadvertently logged out when I submitted it. Thanks for the help, though. And, I’ll be wearing a Hawaiian shirt and jeans on Friday.

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#192476

MBBinWI
Participant

@joanambrose – If you’re logged in with the UID that you submitted it under (which is the one you’re using) then there should be an “Edit” hot link next to the message number.

P.S. Make sure you have your 37 pieces of flair as well!

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#192479

Joan Ambrose
Participant

@MBBinWI- I had to do the test to see if I was human when I posted the original message, which I now understand indicates that I wasn’t logged in. (My other posts have the Edit hot link since I logged in while desperately trying to figure out how to edit the original message.) Apparently, I am human, since I erred. I love how my Reputation is growing because of this . . . we’ll use the term reputation very loosely in this case. By the time I reach Reputation 100, I should be competent at logging in, posting AND editing.

P. S. I always have my 37 pieces of flair!

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#192481

MBBinWI
Participant

@joanambrose – K-State, hmmm. Manhattan is a lovely city during the summer when all the students have gone home to farm. Spent a couple of years there when I worked at that small gov installation just to the west. Probably still have my club card for the bars.

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#192484

Joan Ambrose
Participant

Okay, so even with the error (no pay and zero pay should read straight/regular pay), I think the logic works. When an employee works a day of overtime, a maximum of one day of overtime would be paid, either to that employee or to another employee who subsequently had to work due to a day off being taken in lieu of overtime pay. If more than a day of subsequent overtime is worked and paid, then the logic says that something else is playing in beyond the policy (differing employee skill and productivity, additional work, etc). It’s likely that less than a full day of overtime will be paid, since I imagine there is some negotiation on when that day off can be taken. Or, is there something I’m missing?

When you consider all of the possible permutations on how each overtime work and day off could play out, including a day off at the end of one month leading to overtime at the beginning of the following month, it seems that it would be really difficult to show a strong correlation by shifting by a set number of days. I imagine it’s that complexity that led to the question in the first place.

@MBBinWI – You mean Fort Riley, Home of The Big Red One?

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#192497

MBBinWI
Participant

@joanambrose – That would be the ONE (he, he).
You need an avatar. Here are two. I particularly like the Crescent Beverages one, but Katie probably won’t.

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#192499

Katie Barry
Participant

@MBBinWI – Katie me?? Have you learned nothing about me??? :) That is a great movie. I highly approve.

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#192501

Joan Ambrose
Participant

@MBBinWI
Those are fine choices. In fact, they are such good options, I have to wonder if you know me! I was thinking a laughing Princess Leia could work . . . maybe a laughing Princess Leia, at the age of three, in fuzzy technocolor. (I got that wavy red underline under technocolor, which I now understand means that it is misspelled.)

Yep, that Crescent Brewery picture is right up my alley. But, I don’t think Katie would approve either. (Katie, take another look.) Maybe I could crop out the hand.

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#192502

Katie Barry
Participant

@MBBinWI and @joanambrose I know the image :) The picture would be so small as an avatar. Unless you draw an arrow to, ahem, the relevant section… Who’s really going to notice?

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#192503

Joan Ambrose
Participant

I like Katie.

(Surely this post will put my reputation over 100!?)

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#192504

MBBinWI
Participant

@joanambrose & @KatieBarry – actually, I was thinking about cropping just the hand LOL!!!!!!!!!!!!!

You’d be surprised whom I know. And, yes, we’ve actually met. Now, without additional help, you try to figure out where and who I am. Just don’t divulge on the board. Once you figure out the answer, a means of communication will be readily apparent (and no clues from you, either, Katie).

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#192506

Katie Barry
Participant

@joanambrose Sucking up is an excellent start to earning points. I can also be bought with chocolate. Really good milk chocolate (not a regular Hershey’s bar, and none of that silly dark chocolate nonsense). Hee, hee.

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#192507

Joan Ambrose
Participant

@MBBinWI Okay, that made me laugh! I hadn’t thought we were acquainted. WI is for Wisconsin, yes? (Just checking assumptions.) Is your Avatar actually you or your son, or is it some random baby you found on the internet?

Gotta run. I need to get to the chocolate store before it closes. Don’t tell Katie. I want it to be a surprise.

I sure hope this is helpful to Jeff.

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#192511

MBBinWI
Participant

@joanambrose – Since you’re new here, you haven’t had the experience to see that no thread goes more than 4 replies long before it gets hi-jacked and diverted to who knows where. It’s the fun of the board. (and, yes, that’s a random baby picture – that happened to come from an old photo album from my parents).

@KatieBarry – You just haven’t had the right dark chocolate, yet.

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#192525

Joan Ambrose
Participant

@MBBinWI Some much less than 4 replies long. And, the WI question? Of course, I know where I met you. I’ve managed to eliminate a few suspects. I’m at a huge disadvantage, since my account was shut down briefly, and I lost all contact information. The particular who may elude me for a while, but I’ll figure it out eventually.

Regarding the Avatar, as tempting as the Crescent Beverages one is, I just can’t do it. After all, I am using my real name, and I wouldn’t want to (further) tarnish my Aluminum Reputation, or, more importantly, the reputation of those I’m associated with.

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#192526

MBBinWI
Participant

@joanambrose – believe me, the reputation of SOME of those with whom you associate couldn’t be tarnished any further.

But, alas, yes, using your real name does put a hamper on having fun. One, of many, reasons that I prefer using a nom de plume.

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#192547

Joan Ambrose
Participant

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#192548

MBBinWI
Participant

@joanambrose – too predictable

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#192549

Joan Ambrose
Participant

@MBBinWI As I said, Movie-Buff-Baby-in-Wisconsin, it’s a start. . . and a step up from the bubble-head . . . or is that an airhead? . . . and I REALLY like her . . . and she isn’t an avatar, she just hangs out with avatars . . . and . . . and. . . but. . . but. . .

You can find my more interesting (?) avatars on that well traveled social network. I particularly like the one I just changed into today. I use them more like outfits there, to reflect my mood or the season or what I’m doing. Today’s goes with my mood on this dark, early morning.

So, which film are the images you provided from? I don’t believe I’ve seen it, and I think I need to.

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#192550

MBBinWI
Participant

@joanambrose – as Katie will surely attest, one of the best movies ever – Office Space.

BTW – this is the closest that I come to “social network” use.

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#192661

Dan Dobyns
Participant

I would think you would just look at this as a simple cost/output ratio. If you were able to quantify the end result of what you were doing. i.e. making widgets You would simply compare the months that you used the policy of having a day off with months were you didnt allow a day off.
If that didnt tell you what you wanted to know, then creating two productionpossibility frontier diagrams may be the way to go.
I would look at cost personally, because that is the real impact on the company. You may find that you have too many people in one area and too few in another area. It could also be that you have some people doing multiple tasks and not allowing them to specialize in an efficient way. Sometimes using TOC allows you to see past the paradigm to a better solution.

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