1. Scatter Plots and Regression Lines Without a Calculator

2. What is a Line of Best Fit?
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.

3. 1. Prepare a scatter plot of the data.
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
550
Arch Special with Bacon 34
590
Crispy Chicken 25
500
Fish Fillet 28
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.

4. 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?
                          
Let's find out!
2. Using a straight edge, position it so it is as close to all the points as possible.

5. 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?
Find two points that you think will be on the "best-fit" line. 
Click to see best fit
I chose the points (9, 260) and (30, 530).  You may choose different points. 
Calculate the slope of the line through your two points.             

6. 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?
Write the equation of the line using the slope from step 5.
Substitute x and y
Solve for b.
Final Regression Equation:

7. 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?
Final Regression Equation:
Lets predict how many calories a sandwich would have if it had 22 grams of fat?
So we would predict that a sandwich with 22 grams of fat would have 427 calories.:

8. A Word About Predictions
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.

9. Let’s Practice with This One!
Write the regression equation and predict the value of the investment 10 years after the initial purchase.