1. Scatter plots
Recall:
Coordinate plane- A two-dimensional surface on which points are plotted and located by their x and y coordinates (x,y). This point is made by moving horizontally along the x-axis using the first number in the coordinate pair and then using the second number moving vertically along the y-axis.
Equation of a line- y=mx+b, where x and y are variables that will give you coordinates along the line, and m is the slope of the line, and b is where the line crosses the y-axis.

2. Scatter plots
A scatter plot is a graph of plotted points that shows a relationship between two sets of quantitative data (referred to as bivariate data). Scatter plots are composed of "dots" (points) on a set of coordinate axes. Do NOT connect the dots!
Scatter plots are a popular and effective way of graphing data to display patterns, trends, relationships and an occasional extraordinary value located apart from the other values. (outliers)

3. Scatter plots
Example: Does studying for that Final Exam really help your score? Does one event really affect the other?
The scatter plot at the right appears to show that the longer students studied, the higher their examination scores.
According to this survey of 15 students studying for the same examination, it appears that the answer to our initial question is "yes", studying does affect your score. At least, the answer is "yes", for this particular group of students.

4. Scatter plots
Notice how the data in the graph resembles a straight line rising from left to right. When working with scatter plots, if is often useful to represent the data with the equation of a straight line, called a "line of best fit", or a "trend" line. Such a line may pass through some of the points, none of the points, or all of the points on the scatter plot.

5. Scatter plots: Line of Best Fit
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
Example: Is there a relationship between the fat grams and the total calories in fast food?
Paper and Pencil Solution: 1.  Prepare a scatter plot of the data on graph paper.
2.  Using a strand of spaghetti, position the spaghetti so that the plotted points are as close to the strand as possible   Find two points that you think will be on the "best-fit" line.    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. Scatter plots: Line of Best Fit
Example continued:
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: calories

7. Scatter plots: 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?

8. Scatter plots: 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.