# Exploring Linear Function Models (Grade 9 – Ontario) Student Handout

A downloadable version of this activity is available in the following format:

Over the next few days, you will be

• completing an online census questionnaire
• requesting data from an online random data selector
• modelling data with linear functions
• creating and presenting your own data story

### Completing an online census questionnaire

After your teacher tells you the story behind the Census at School project, go to www.censusatschool.ca Click on the “Student” button and fill in the online questionnaire, using the class ID and password that your teacher gives you.

### Requesting data from an online random data selector

Refer to your PowerPoint Instructions handout.

Step 1: Request a dataset of 100 14-year-olds from the Census at School website in the United Kingdom.

Do this at home. Save the file on a disk and bring the disk to school.

### Modelling data with linear functions

Use your data file on disk and the PowerPoint instructions.

Step 2: Import the dataset into a statistical software environment (i.e., Fathom).

Step 3: Construct a scatterplot.

Step 4: Use a movable line (an informal process) to fit a linear functional model to your scatterplot.

For steps 5 to 9, insert a text box to type in your comments.

Step 5: Find the least squares line. Reflect on what the r^2 value suggests about the appropriateness of this linear model.

Check out an online Java Applet that helps you understand where the least squares line comes from at www.keypress.com/sketchpad/java_gsp/squares.html.

Step 6: Reflect on the meaning of slope (m) and y-intercept (b) in the equation of your linear model, y=mx+b.

Step 7: Reflect on the strengths and weaknesses of your linear model.

Step 8: Use a filter to explore whether a linear model of just boys or just girls gives a stronger correlation.

Step 9: Use a filter to explore whether a linear model of each country individually gives a stronger correlation.

Be sure to save your work.

### Creating and presenting your own data story

Step 10: Select two numeric attributes/variables that you think could be modelled with a linear function.

Step 11: Construct a scatterplot and fit a movable line to your data.

Step 12: Find the least squares line.

Step 13: Experiment with filtering subgroups (by gender, country, etc.) to improve your r^2 value.

Step 14: Using presentation software (Corel Presentation or PowerPoint), create your data story, including your data displays.

Step 15: In your data story, include reflections on the strength(s) and weakness(es) of your linear model(s).

Be sure to save your work.

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