Linear Regression

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Linear Regression

Activities

Looking at the Data

Worksheets

Using Statistics in Human Movements

Student Generated Linear Data

Olympic Gold Medal Performances

Datasets
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Java Applets

Linear Regression

The study of functions in Maths B can be enriched by including authentic applications which illustrate how mathematics can model aspects of the world. In real life functions often arise from data gathered from experiments or observations, and such data rarely falls neatly into a straight line or along a curve. There is variability in real data that needs to be explained and measured, and it is the task of the student to find the function that best 'fits' the data in some sense.

The first functions we study in Maths B are linear, so it makes sense to start with problems that are whose data are linear in nature.

Looking at the Data

When fitting a function to data, the student MUST first plot the data, and this activity shows why. F.J. Anscombe invented these datasets to demonstrate the importance of graphing the data before finding the correlation and line of regression. They present a very striking picture.

Using Statistics in Human Movements

One measure of form for a runner is stride rate, defined as the number of steps per second. A runner is considered to be efficient if the stride rate is close to optimum. The stride rate is related to speed; the greater the speed, the greater the stride rate. This article gives a fully-worked solution to finding the stride rate as a function of speed using the statistics functions of the TI-83 graphics calculator.

Student Generated Linear Data

At times we should use real data, gathered to give insight into real problems, as this illustrates how fitting a function to data may be done in real-life. But we should also get our students to generate their own data, which gives them ownership of the data and an understanding of the process (often difficult) of collecting reliable and valid data. This article contains examples from high schools in the U.S.

Olympic Gold Medal Performances

The Olympics coming to Australia in the year 2000, so datasets about the Oympics are worth their weight in gold medals. In this worksheet the data for the gold medal performances in long jump, high jump, discus throw since 1896 are supplied. Students are asked to find a linear model for each set of data, and predict the gold medal performance in Sydney in the year 2000.

Linear Regression Java Applet

This applet teaches students the effect on a regression line of adding an additional point.

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