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Here are some questions for discussion:
• “How does using technology help model the data in the scatter plot?” (It allows di erent people to come up with the same equation for the line of best t. If the line is just drawn by hand, there can be di erent linear equations that seem to t the data well, but there is only one “best” t line.)
• “What does the -intercept represent in each scatter plot? When is it reasonable to use this interpretation?” (It represents the value of estimated by the linear model when . When the intercept is near the range of the data it can be reasonable to use this interpretation, otherwise the linear trend may not continue.)
• “Why is the slope the same in scatter plot A and scatter plot F” (It is the same because the data in scatter plot F is the same data as scatter plot A, except that the values for have all been increased by 4.5 units.)
Tell students that they should be careful when predicting values outside of the range of the data, in particular for the -intercept. Even when the data is t well by a linear model, the behavior of the variables farther away may not be linear. It is important to remember that all predictions using the best t line are estimates and the reasonableness of the predictions should be considered.
Lesson Synthesis
Here are some questions for discussion.
• “What is a line of best t?” (The best linear model for the data.)
Unit 3 Lesson 5: Fitting Lines 77