Discovery & Exploration: Spaghetti Models

By the end of this activity, you will determine if there is a relationship between fat grams and the total calories in fast food. Work with your partner.

Step 1: Given the following data set, create a scatterplot using graph paper and pencil. Include a title for the graph and label the axes.

Fat Grams Calories Sandwich (x) (y) BK Hamburger 12 290 BK Whopper 37 650 BK Chicken Sandwich 36 640 McD Hamburger 9 250 McD Quarter Pounder 26 520 McD Chicken Sandwich 33 510 5 Guys Little Burger 26 480 5 Guys Burger 43 700 Wendy's Jr. Hamburger 8 230 Wendy's ¼ lb Burger 31 580 Wendy's Chicken Sandwich 19 350 Chick-fila Chicken Sandwich 18 440

Step Two: Position a piece of spaghetti so that the plotted points are as close to the spaghetti as possible. This will accurately reflect the line of best fit for the data set. Step Three: Find two points that lie on your line of best fit that most accurately reflect the data. Some groups may choose different points. Step Four: Calculate the slope of your two points, rounding to the nearest hundredths place. Step Five: Use your slope and choose a point from the data. Use point-slope form to find the equation of the line in slope intercept-form. You may also use the slope and a point to find the y-intercept and then rewrite the equation in slope-intercept form. Step 6: Compare your equation with other groups. Did you obtain similar results? Is there a correlation between fat grams and number of calories? If so, what is the correlation? What does the slope of your line represent in terms of the relationship between fat grams and calories? Answer Key

Student models should resemble the following graph. The linear regression equation is 13.48x + 135.26.

There is a positive correlation between fat grams and calories. The slope indicates that as the number of fat grams increases, the calories also increase.

Extension:

If time permits, students may use graphing calculators to find the line of best fit as an extension activity. Teachers may also choose to use Geogebra to model the linear regression to the class.