1. Lesson 2

1.5. Explore

Mathematics 30-2 Module 4

Module 4: Polynomials

 

Explore

 

You may have discovered in Share 1 that different people may determine different lines of best fit. Your lines were probably similar, but not exactly the same. The reason for this is that there is a trend to the data, but no exact line that goes through all data points.

 

algorithm: a specific set of steps for finding a solution to a problem

Mathematicians have created algorithms for creating the equations of lines that truly are “best” fit for the data. These algorithms minimize the difference between points in the scatter plot and points on the line. The resulting equation is called a regression equation and can be treated as a line of best fit. These algorithms have been implemented in spreadsheet programs and graphing calculators.

 

Once you have a regression equation, it can be used to answer questions for the problem.

 

tip

Refer to the statistics section of your calculator’s manual to determine how to create regression equations. You will need to find a method to do the following:

  • Clear all lists so you are sure that you start with no data in the lists.
  • Enter lists of data.
  • Create a linear regression equation. (Look for “y = ax + b.”)

If you have difficulty with any of these steps, contact your teacher for assistance.

 





assessment
Try This 2

 

Enter the data from the table on page 295 of your textbook into your calculator; the data is also shown in the Discover. Enter the height values as the first list and the hand span values as the second. If you have difficulty with any of the steps in determining a linear regression equation, consult your calculator manual or contact your teacher.

  1.  
    1. Now perform the steps to find the linear regression equation.
    2. How does this regression equation compare to the equation of the line of best fit you determined in Try This 1?
  2. Use your regression equation to predict the hand span for a person who is
    1. 140 cm tall
    2. 160 cm tall

course folder Save your responses in your course folder.

The linear regression equation for the hand span problem is y = 0.23x − 18.30, where x is height in centimetres and y is hand span in centimetres. If this equation is different than yours, make sure your data was input correctly. If it is still incorrect, check that the height is represented by x-values and that the hand span is represented by y-values.