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Mathematics and Statistics are quite far behind in my educational curriculum, and yet now I seem to need them again, so this set of questions is very basic I suppose:

What is a trend line? What various types of trend lines are there? And what are their respective use or relevance?

Background:

I'm working on a thesis and I am producing some visual rendering of a survey I ran, in which I tried to measure public knowledge of (colonial) history and heritage in a town of Kerala, India.

I have data for instance, representing the result of a test, the average result of which is compared to various criteria of the population (age, education, etc.) With regard to criteria such as age-group, income or education, it is also interesting to find out whether their increase improves the results.

I am working on this data with LibreOffice, which offers me the possibility to show a "trend line", and I suppose the trend-line is adequate to show the relation between x and y, i.e. criteria and result. However, there are 4 types of trend lines available: linear, logarithmic, exponential and power.

Which one should I chose? Which difference does it make? How would I figure out a trend line if LibreOffice would not do it for me?

Wikipedia brings some light on those questions. Although I am not sure whether I should look at linear regression or technical trend line analysis.

Could you please provide a short "Trend Line for Dummies" introduction? Thanks :)

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    $\begingroup$ Benjamin, I would encourage you to go find a grad student in statistics that would consult with you. There is a lot more to this than simply having a spreadsheet create a trend line. There are a lot of considerations around how well does the line fit, how significant are the criteria you are using, etc. You need someone with a good knowledge of regression analysis to do this right. If you're writing a thesis you're going to need solid stats behind your conclusions. $\endgroup$ – Dave Kincaid Aug 17 '11 at 17:40
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    $\begingroup$ Your question is very sincere, but you're essentially asking "Hey, I have this large device in my basement that has a big tank of gasoline or something connected to it, and there's this big red button on it I want to push. What will it do?" Especially at the graduate level, you can't just make a choice from a list of four options and expect that any of the choices are applicable or that any of the results are meaningful. +10 on the suggestion to take your data to someone who is good with statistics. $\endgroup$ – Wayne Aug 17 '11 at 17:58
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    $\begingroup$ Have a look at LibreOffice's internal help. There you will find an explanation of these different types of lines. If that sounds unintelligible to you, follow the advice you should get familiar with linear regression. Or consult a statistician if you are not sure ... $\endgroup$ – user5644 Aug 17 '11 at 18:02
  • $\begingroup$ Thanks guys for your input. What I am doing here is in fact beyond what is asked of me, but I like to learn. I'll see if I can find someone studying statistics, it might indeed be a good idea. $\endgroup$ – Benjamin Aug 17 '11 at 19:08
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    $\begingroup$ @Benjamin: great that you want to learn more than is required of you! Just wanted to emphasize that the comments you're getting are a reflection of how truly complicated your question is, under the surface, and how much the answer depends on many specifics of your data, your knowledge, and your goals. Not criticisms of you. $\endgroup$ – Wayne Aug 17 '11 at 21:12
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A trend line is an expression, in mathematical form, of the relationship between your data - lets say in your case, knowledge and income. The assumption is there is some mathematical relationship between the two - lets say for every increase of $100 in annual income, your score on a hypothetical test goes up by one. Now that's not what you'll see in the actual data, because there's some random variation in the data. What a trend line does is tries to fit the data as best it can to give you an idea what the actual relationship is.

The difference between various trendlines comes from what shape the line is allowed to take. For example, a linear trendline must be a straight line - you're saying there is a linear relationship between your variables. An exponential line is a little more flexible, as it says that the relationship of one variable is found with some exponent of the other variable - that exponent can be 1, where you get a straight line, or it could be something else.

If you are simply trying to summarize your data, and give the viewer of the graph some idea of the relationship that exists between them, a linear or exponential trendline should be fine. For questions beyond that, it would be useful to know what you'd like to say about the two variables, but at that point, you may be well served by going to talk to someone in your department who works more heavily with statistics.

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    $\begingroup$ +1 for finding someone else who works more with statistics $\endgroup$ – Dave Kincaid Aug 17 '11 at 17:46

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