# Predicting future numbers of students

G

#### Guest

##### Guest
Student numbers have increased annually for five years (130,143,159,189,227). I have to predict next 3 years by using linear N=ax+b. (I think I can graph this by guessing at a linear increase through plotting (a) and b would be my start number of students?, x is number of years from start? )

But then I have to use quadratic model N=axsquared +bx+c. How do I estimate the values for constants a,b,c ? Is c the start number of 130? x again the year? a the increase then I solve for b?

How do I graph it on computer please?

Probably too many questions at once.

I do hope you can help. I have been guessing round this for ages. Annemarie

#### tkhunny

##### Moderator
Staff member
There are quite a few ways to proceed, but I think I haven't enough information to provide the right kind of direction.

What class are you in? Algebra? Statistics? Economics?
What methods can we use? Regression? Least-Squares? Eye-ball?
What level are you? Algebra? Calculus?

G

#### Guest

##### Guest
Predicting student numbers

Thanks for getting back to me so quickly. From problems to algebra manipulation is the title of Unit. Course booklets are on investigations and factors.

I have been asked to plot a graph showing the number of participating students over time. For each model (linear, quadratic) I am to estimate values for the constants and predict numbers for the following three years.
Then discuss the appropriateness of each model.

I can see that I shall need to estimate increase factor but pretty sure that one constant has to be my start number of students. I have been estimating and factoring prior to drawing the graph but suspect I should be drawing the graph first.

Cannot see either solution as appropriate.

Supposed to be higher algebra but I'm pretty intermediate minus.

Annemarie :roll:

#### tkhunny

##### Moderator
Staff member
Well, that doesn't exactly clear up the intended methodology. I'm kind of torn how to proceed, but I'm leaning toward my favorite "Quick and Dirty" solution to such problems, a spreadsheet!

If Y = Years since the beginning of the survey and S = Students:

Drawing a line, I get S(Y) = 24*Y+97.6
S(6) = 241.6
S(7) = 265.6
S(8) = 289.6

Strength: Simple.
Weakness: Data don't really suggest a linear relationship.
Weakness: Projections ONLY increase, EVER! That can't be right.
Weakness: Confusing NonInteger values. Just who is that 0.6 student?

Drawing a quadratic, I get S(Y) = 4.5714*Y<sup>2</sup> - 3.4286*Y + 129.6
S(6) = 273.6
S(7) = 329.6
S(8) = 394.7

Strength: Simple, but not as simple as linear.
Strength: Really NAILS the data.
Weakness: Projections ONLY increase, EVER, and WAY faster than the linear model. That REALLY can't be right.
Weakness: Confusing NonInteger values. Just who is that 0.7 student?

I really can't tell you how I arrived at these particular models. It was a normal mathematical procedure that is beyond the scope of your course. You may wish to use some averaging technique to create other equations,

-- Maybe use points 2 and 4 to define a unique line
-- Maybe use points 1, 3, and 5 to create a unique quadratic

G

#### Guest

##### Guest
Thrown offline all the time yesterday before I could get a good look at this or say thankyou. Really pleased that the linear trials I had done more or less match up. Have been doing simultansous equations to colve the quadratics but had done 123, 234, 345. One of these comes pretty near your solution but totally whole numbers .Never thought of 135 --now that really makes sense.

I figure the linear solution you have --which was my excel model -- gets the 24 as an average of the total differences between years?

So far, so very good thanks. But I may well be back.... AnneMarie