$$\DeclareMathOperator{cosec}{cosec}$$

Statistics and Probability

Syllabus Content

Equation of the regression line of x on y. Use of the equation for prediction purposes

Here is an exam-style questions on this statement:

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

Furthermore

Official Guidance, clarification and syllabus links:

Students should be aware that they cannot always reliably make a prediction of y from a value of x, when using an x on y line.

The regression line of $$x$$ on $$y$$, often denoted as $$x = f(y)$$, is a statistical tool used when $$y$$ is considered the independent variable and $$x$$ is the dependent variable. This is less common than the conventional regression of $$y$$ on $$x$$, but it is useful in situations where we are interested in predicting the value of $$x$$ given $$y$$. For example, one might use the regression of $$x$$ on $$y$$ if $$y$$ is time and $$x$$ is a process that unfolds over time.

The equation for the regression line of $$x$$ on $$y$$ is given by $$x = a + by$$, where $$a$$ represents the intercept and $$b$$ the slope of the regression line. The slope indicates the change in $$x$$ for a one-unit change in $$y$$. It is important to note that this does not imply causation; rather, it is a way of describing how the two variables co-vary. To compute the coefficients $$a$$ and $$b$$, one would typically use the method of least squares, minimising the sum of the squares of the vertical distances of the points from the line - best done on a GDC.

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.

For Students:

For All: