Oct 12 2024

Correlation and Regression

Try out the new table regressions in Desmos. This is so easy to use; I copied data from a spreadsheet and pasted it into a blank expression line. To create a regression, simply click the Add Regression icon to the left of your expression. I tried the Desmos table regression using a data set from this new Transum Activity, Odd Scatter Out, where students have to identify the odd one out from a set of 5 scatter diagrams. Link to Desmos page.

For more on Statistical functions with Desmos, see this article from the Desmos Help Centre.
Keep an eye on this Desmos playlist to see what’s new.

Further resources for correlation and regression:

This GeoGebra applet allows students to move points and watch the effect on the line of best.

This can be used in class by asking students to plot the points, draw their lines of best fit and then comparing with the computer. This worked really well on my phone, I simply sent myself an email with the link and was able to move points easily. This could also be used with younger classes when talking about lines of best fit.

We can also demonstrate correlation coefficients and lines of best fit with this PhET simulation on Least Squares Regression.

Correlation & Line of best fit — PhET – Least Squares Regression

Choose from a range of examples or choose Custom to add your own points and guess then check the correlation coefficient. You can also draw your own line of best fit and compare it to the theoretical line of best fit. Note the option to include residuals for both your own attempt and the line of best fit.

We can check Regression Calculations using this Linear Regression calculator from Social Science Statistics.

On the subject of correlation coefficients, we can play a game to see how well we can guess the correlation coefficient! Guess the Correlation Coefficient.

From Cambridge PhD student, Omar Wagih ‘Guess the Correlation‘, a rather addictive game with a purpose – Omar Wagih is collecting the data on the guesses collected and using it to analyse how we perceive correlations in scatter plots. Select About to read the rules and further details.

We also need to look at ranked data and students must be able to calculate Spearman’s rank correlation coefficient from raw data or summary statistics. Again, Social Science Statistics, offers us a calculator which will be useful for checking work.

Spearman's RanK Calculator — Social Science Statistics

Calculation details provide a useful check on work.
Note Social Science Statistics also has a calculator for calculating the Pearson correlation coefficient.

Dec 27 2020

Tidying Up!

A break is always a good time for tidying up and reorganising things!

Continuing the Use of Technology series of pages, the PhET Simulations, Standards Unit Software and Wolfram Alpha pages have been added to the series.

Added to the GeoGebra series is a new page, GeoGebra Resources-Edexcel so all the resources for GCSE and A level Maths and Further Maths are available in one place.

A recent addition to the top menu includes Updates where updates to popular posts are noted. A further new page added today is Popular Posts and Links, just a small number of currently popular posts and/or files. I see that the file of legacy coursework tasks from Edexcel has proved very popular this year as has The Workers of Zen.

Feb 10 2018

For Valentine’s Day…

Checked and updated annually, this page has ideas and resources for Valentine’s Day …

Jan 28 2018

Mathematical Miscellany #18

crashMATHS has some very useful free resources for GCSE and A Level; the site is under development but you will find plenty of useful resources already. Checking for some additional resources on Completing the square for my Year 10 students I came across a GCSE worksheet from crashMaths; this has a good variety of questions including questions to stretch your students aiming at the highest grades. The worksheet solutions are noted as coming soon. For a topic such as completing the square, this is an ideal time to use technology to check our work. Any of Desmos, GeoGebra and WolframAlpha could be used. (Select for Desmos page.)

Staying with crashMATHS, note the A Level Practice Papers and mark schemes, this looks like a very valuable resource. There are several papers and mark schemes available with more coming. Versions are provided for AQA and Edexcel, these use the style of papers we see from the exam boards. Currently, there is nothing for OCR. For Mathematics the content is the same for all the boards and for Further Mathematics we have a prescribed core which must comprise approximately 50% of its content. This common content as we have with GCSE is very useful indeed as we can use resources from all the examination boards.

Continuing with an A Level theme we have a very interesting read, published 25th January 2018, “An evaluation of the item difficulty in AS and A level maths“. This compares the difficulty of items in sample AS and A level maths assessment materials from 2016 and 2017 with the A Level papers from 2015. The overall objective of the exercise was to compare the profile of item difficulty within the SAMs with that of the corresponding 2015 assessments, a question I believe is on the minds of Maths teachers!

Ofqual: Expected item difficulty Legacy & Reformed Specs

Clearly, we can look at the specimen materials ourselves and make our own judgement on the difficulty but this seems a robust study which used Comparative Judgement. This is a technique where each reviewer reviews many pairs of items and decides each time which item is more difficult to answer.

Items from the sample assessment materials submitted for 4 specifications, AQA, MEI, OCR and Pearson were used.

The study shows slightly higher levels of expected difficulty for items from the sample assessments relative to the 2015 assessments but the increase in difficulty is small. The paper states that ‘Such small differences can easily be accommodated by the setting of grade boundaries at awarding. The choice of specifications to teach should be based more on content and style as there is little appreciable difference in difficulty.’

For further reading on Comparative Judgement, look at the work of Daisy Christodoulou.

If you have not yet signed up for the new home of Edexcel’s Maths Emporium then do so! This is such a valuable resource. Latest additions include some great new GCSE maths practice papers. There is a wonderful set of practice papers by topic. Look first at GCSE Mathematics, then choose Cabinet 11 for the current specification. Under Practice Papers you will find the themed set – brilliant!
Emporium Resource

To finish this collection, from NCETM look at their Secondary Assessment materials which have been written to support teachers in making judgements on the degree to which pupils have mastered various components of the KS3 mathematics curriculum. This follows the primary Mastery Materials, which was published in 2015.

See further posts in the Mathematical Miscellany Series.

Nov 12 2017

Integration – Desmos & WolframAlpha

With my year 12 students (UK age 16-17) we have been looking at definite Integration. Desmos and WolframAlpha are both excellent for checking work and by using the technology we have a very clear visual representation adding to our understanding.

One of the homework questions for my students involves finding the total shaded area bounded by f(x) = x⁴−3x³−4x²+12x, the x-axis, the line x=−1 and the line x=3.

We could use WolframAlpha for a quick check. I like the visual representation showing students clearly that they are dealing with areas above and below the x-axis.

Scrolling down the page we see that this query also returns the indefinite integral.

For the total shaded area, students could change the limits of the query to evaluate each section.