I am trying to find the best method to model the population growth in a school. In my possession I have the student count by semester in the last 16 years. Moreover the first information I consist of a growth from 2510 to 7213 students. Any recommendations as to which method I can use to model this growth and that will help me make predictions of the population in the future. I am currently looking in regression and the logistic model.
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1$\begingroup$ Hi, welcome to Math.SE. Please indicate what you have tried and where you are stuck. This will help people better tailor their answer to your background and situation. It will also demonstrate that you are interested in your question and not just looking for someone to do your homework for you - Math.SE is not a homework site. $\endgroup$– Ian MillerCommented Apr 9, 2016 at 3:34
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$\begingroup$ But... Doesn't the population in a school depend primarily (say) on the infrastructure? If 16 years ago there were 2500 students and today there are 7200, I'd say it's most likely because the school bought a new building. Which cannot really be predicted, I think. $\endgroup$– G. SassatelliCommented Apr 9, 2016 at 3:41
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2 Answers
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Population growth in a school tends to be influenced by external factors (how the local economy is doing, how the neighbourhood is changing, changes in school boundaries, construction of additional classrooms or portables, ...). Over a 16 year period, I very much doubt that it could be modeled very well by any simple model, such as a logistic model. You might be able to use linear regression to try to fit a curve with a few parameters, say a polynomial.
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$\begingroup$ Yes, in fact there have been several additional constructions over the time which indicate a growth in the school population. I am trying to make predictions of future populations. As far as the logistic model you are right, I have researched and tried to work around it but it does not work. I have done as you suggested and used linear regression to find the line of best fit in polynomial. I got the following however I'm currently working on finding if this polynomial will be useful to find predictions of the population over a period of time. $\endgroup$ Commented Apr 13, 2016 at 12:54
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$\begingroup$ I found Σ xi = 40,110 , Σ yi = 95652 , Σ xi yi = 179190915 and Σ xi 2 = 80441270 and n = 20 Substituting, I get 95652 = 20a + 40110b 179190915 = 40110a + 80441270b by solving these two equations I get a = 578523909.521 and b = 288466.278195 which gives me the following: y = 578523909.521 + ( 288466.278195 ) x $\endgroup$ Commented Apr 13, 2016 at 12:56
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@earth_space, Logistic regression will not work here at all. It's used when you have some categorical variable as dependent.
you need to see variation in data and then you can use linear Regression analysis.here are the assumption of regression-
http://www.statmethods.net/stats/rdiagnostics.html
Other possible time series algos must also be checked starting from AR, MA, ARMA and ARIMA etc.
answered Apr 9, 2016 at 4:28
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1$\begingroup$ Logistic population growth models are a fundamental building block in population biology. $\endgroup$– AlexisCommented Jan 22, 2020 at 18:00