Texarkana Independent School District



When data is displayed with a scatter plot, it is often useful to attempt to represent that data with the equation of a straight line for purposes of predicting values that may not be displayed on the plot.

Such a straight line is called the “line of best fit.” It may also be called a “trend line”.

Materials needed: graph paper and a strand of spaghetti

Question(s):

Is there a relationship between the fat grams and the total calories in fast food?

Can we predict the number of total calories based upon the total fat grams?

|Sandwich |Total Fat (g) |Total Calories |

|Hamburger |10 |260 |

|Cheeseburger |14 |320 |

|Quarter Pounder |22 |420 |

|Quarter Pounder with Cheese |30 |530 |

|Big Mac |31 |560 |

|Arch Sandwich Special |31 |550 |

|Arch Special with Bacon |35 |590 |

|Crispy Chicken |25 |500 |

|Fish Fillet |28 |560 |

|Grilled Chicken |21 |440 |

|Grilled Chicken Light |6 |300 |

Instructions:

1. Prepare a scatter plot of the data.

2. Using a strand of spaghetti, position the spaghetti so that the plotted points are as close to the strand as possible.

3. Find two points that you think will be on the “best-fit” line.

4. Calculate the slope of the line through your two points.

5. Write the equation of the line. y – y1 = m(x – x1)

6. Use the equation to predict information that was not plotted in the scatter plot.

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Activity I: Line of Best Fit

(without graphing calculator)

Predicting

• If you are looking for values that fall within the plotted values, you are interpolating.

• If you are looking for values that fall outside the plotted values, you are extrapolating.

• Be careful when extrapolating. The further away from the plotted values you go, the less reliable your prediction will be.

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