Project: Data Analysis Do you ever think about the number of calories in your favorite foods? Maybe ice cream is better for you than a hamburger. One way to find out would be to figure out how many calories and grams of saturated fat are in both foods. Typically, foods have nutritional information like this on the packaging. Or if you eat out, many fast food places will provide this information. Once you have collected the data, you can begin to analyze it.

OBJECTIVES

Collect, organize, and analyze data.

Make predictions based on data.

According to the U. S. Food and Drug Administration, 30% of daily calories should come from fats and only 10% from saturated fats. Based on a 2,000-calorie-a-day intake, this translates to about 600 calories from fat and 20 grams of saturated fat.

By knowing the number of fat calories in a fast food item, can you predict the number of grams of saturated fat?

I. Collect data from several fast-food chains on the number of fat calories and grams of saturated fat in menu items. A record at least 12 ordered pairs of (fat calories, grams of saturated fat). Organize your data in a table.

II. Make a scatter plot of the data on graph paper. Be sure to label the axes and use an appropriate title for the graph.

You may wish to use a graphing calculator, spread sheet, or other technology resource (such as the graphing utility link below) to aid you in graphing.

III. Draw a trend line for the scatter plot. Use the following scatter plot of the ordered pairs (fat grams, total calories) as an example.

IV. Calculate the slope of the trend line. (Choose two points on the line and find vertical change over horizontal change.)

Note: Graphing calculators and spread sheets have features with which to draw trend lines and determine the equation. You may choose to use one of these options. If you use technology, indicate what steps were taken to arrive at your equation.

V. Using the slope and y-intercept, write the equation of the trend line ( y = mx + b).

VI. Choose a "calories from fat" value that is not in your collected data set and that is at least 10 fat calories away from any collected value. Use the equation calculated in step V to predict the number of fat grams in an item having that number of fat calories. Be sure to show your work.

VII. Search for an item in a fast food menu having the same number of fat calories as the one you chose above. (If you cannot find the exact value, get as close as you can.) Compare the calculated value from step VI to this actual value. Explain why (or why not) you would have expected your prediction (calculated value) to be close to the actual value.