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If you are a teacher then please also visit my new site: intermathematics.com for over 2000+ pdf pages of resources for teaching IB maths!

Predicting the UK election using linear regression

The above data is the latest opinion poll data from the Guardian.  The UK will have (another) general election on June 8th.  So can we use the current opinion poll data to predict the outcome?

Longer term data trends

Let’s start by looking at the longer term trend following the aftermath of the Brexit vote on June 23rd 2016.  I’ll plot some points for Labour and the Conservatives and see what kind of linear regression we get.  To keep things simple I’ve looked at randomly chosen poll data approximately every 2 weeks – assigning 0 to July 1st 2016, 1 to mid July, 2 to August 1st etc.  This has then been plotted using the fantastic Desmos.

Labour

You can see that this is not a very good fit – it’s a very weak correlation.  Nevertheless let’s see what we would get if we used this regression line to predict the outcome in June.  With the x axis scale I’ve chosen, mid June 2017 equates to 23 on the x axis.  Therefore we predict the percentage as

y = -0.130(23) + 30.2

y  = 27%

Clearly this would be a disaster for Labour – but our model is not especially accurate so perhaps nothing to worry about just yet.

Conservatives

As with Labour we have a weak correlation – though this time we have a positive rather than negative correlation.  If we use our regression model we get a prediction of:

y = 0.242(23) + 38.7

y = 44%

So, we are predicting a crushing victory for the Conservatives – but could we get some more accurate models to base this prediction on?

Using moving averages

The Guardian’s poll tracker at the top of the page uses moving averages to smooth out poll fluctuations between different polls and to arrive at an averaged poll figure.  Using this provides a stronger correlation:

Labour

This model doesn’t take into account a (possible) late surge in support for Labour but does fir better than our last graph.  Using the equation we get:

y = -0.0764(23) + 28.8

y = 27%

Conservatives

We can have more confidence in using this regression line to predict the election.  Putting in the numbers we get:

y = 0.411(23) + 36.48

y = 46%

Conclusion

Our more accurate models merely confirm what we found earlier – and indeed what all the pollsters are predicting – a massive win for the Conservatives.  Even allowing for a late narrowing of the polls the Conservatives could be on target for winning by over 10% points – which would result in a very large majority.  Let’s see what happens!

Essential Resources for IB Teachers

1) Intermathematics.com

If you are a teacher then please also visit my new site.  This has been designed specifically for teachers of mathematics at international schools.  The content now includes over 2000 pages of pdf content for the entire SL and HL Analysis syllabus and also the SL Applications syllabus.  Some of the content includes:

1. Original pdf worksheets (with full worked solutions) designed to cover all the syllabus topics.  These make great homework sheets or in class worksheets – and are each designed to last between 40 minutes and 1 hour.
2. Original Paper 3 investigations (with full worked solutions) to develop investigative techniques and support both the exploration and the Paper 3 examination.
3. Over 150 pages of Coursework Guides to introduce students to the essentials behind getting an excellent mark on their exploration coursework.
4. A large number of enrichment activities such as treasure hunts, quizzes, investigations, Desmos explorations, Python coding and more – to engage IB learners in the course.

There is also a lot more.  I think this could save teachers 200+ hours of preparation time in delivering an IB maths course – so it should be well worth exploring!

Essential Resources for both IB teachers and IB students

1) Exploration Guides and Paper 3 Resources

I’ve put together a 168 page Super Exploration Guide to talk students and teachers through all aspects of producing an excellent coursework submission.  Students always make the same mistakes when doing their coursework – get the inside track from an IB moderator!  I have also made Paper 3 packs for HL Analysis and also Applications students to help prepare for their Paper 3 exams.  The Exploration Guides can be downloaded here and the Paper 3 Questions can be downloaded here.