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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!

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All content on this site has been written by Andrew Chambers (MSc. Mathematics, IB Mathematics Examiner).

### New website for International teachers

I’ve just launched a brand new maths site for international schools – over 2000 pdf pages of resources to support IB teachers.  If you are an IB teacher this could save you 200+ hours of preparation time.

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