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.

A line of best fit is a straight line that best represents the data on a scatter plot. 
This line may pass through some of the points, none of the points, or all of the points.


Materials for examining line of best fit: 
graph paper and a strand of spaghetti

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

Sandwich Total Fat (g) Total Calories
Hamburger 9 260
Cheeseburger 13 320
Quarter Pounder 21 420
Quarter Pounder with Cheese 30 530
Big Mac 31 560
Arch Sandwich Special 31 550
Arch Special with Bacon 34 590
Crispy Chicken 25 500
Fish Fillet 28 560
Grilled Chicken 20 440
Grilled Chicken Light 5 300

 

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

Let's find out!

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.
 

            Our assistant, Bibs, helps position
                    the strand of spaghetti.
3.  Find two points that you think will be on the "best-fit" line. 

4.  We are choosing the points (9, 260) and (30, 530).  You may choose different points. 

5.  Calculate the slope of the line through your two points.
            
       
rounded to three decimal places.

6.  Write the equation of the line.
             

7.  This equation can now be used to predict information that was not plotted in the scatter plot.
    Question:  Predict the total calories based upon 22 grams of fat.
         
     
ANS:  427.141 calories

        Choose two points that you think will
                    form the line of best fit. 

 

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 is your prediction.

 

 

So who has the REAL "line-of-best-fit"? 

In step 4 above, we chose two points to form our line-of-best-fit.  It is possible, however, that someone else will choose a different set of points, and their equation will be slightly different. 

Your answer will be considered CORRECT, as long as your calculations are correct for the two points that you chose.  So, if each answer may be slightly different, which answer is the REAL "line-of-best-fit?

To answer this question, we need the assistance of a graphing calculator.  See the next lesson.