Linear Regression Lines (Cambridge (CIE) IGCSE International Maths)

Linear Regression Lines

What is a linear regression line?

• Statistical software can calculate the equation for an 'ideal' line of best fit

  • This 'ideal' line of best fit is known as a regression line

    • It is more accurate than a line of best fit drawn by eye

  • You will be expected to use your graphic display calculator to generate the equation of linear regression

    • You do not need to calculate the equation by hand

• An equation of a linear regression line is usually given in the form

  • is the y-intercept of the regression line

  • is the gradient of the regression line

  • Both of those have the same meaning that they do for any line of best fit

How do I find the equation of a regression line using my graphic display calculator?

• You can find the equation of a line of regression using your graphic display calculator by doing the following:

• STEP 1
  Add your raw data to a spreadsheet in your graphic display calculator

  • On some models, you must enter it in statistics mode

  • The data should be added as two columns

  • Label the columns if you are able (e.g. time, length) or x and y

• STEP 2
  From the statistics function on your graphic display calculator, select the statistics calculations

  • Choose the option linear regression

  • On some models you instead select CALC followed by REG

    • You must also then select X, as we are finding a linear model, rather than quadratic or cubic etc

    • Then select ax+b for the format of the equation

• STEP 3
  Assign the correct columns into your spreadsheet for the x and y lists

  • This is why labelling your columns at the start is important

  • Some models may simply assume the first column contains the x values

• STEP 4
  Write down the values for and produced by your calculator

  • Round each of the values to 3 significant figures (unless they can be written exactly)

• STEP 5
  Substitute the values for and into the equation

How do I use and interpret the equation of a linear regression line?

• You may be asked to draw a regression line onto a scatter diagram

  • You need to know two points on the line

    • Choose two values (they don't need to correspond to any data values!)

    • Substitute these into the equation of the regression line to find the corresponding values

  • Plot these two points on the scatter diagram and draw a straight line through them

    • Use a ruler!

• A regression line drawn from its equation will always go through the mean point, for the data set

  • You may be required to use this fact in an exam question