1. Scatter Plots

2. Scatter plots A graph that relates data from two different sets.
To make a scatter plot, the two sets of data are plotted as ordered pairs

3. Positive Correlation Tilts up to the right
Both sets of data increase together
Both sets of data decrease together

4. Negative Correlation Tilts up to the left
One set of data goes up while the other set goes down

5. No Correlation Data sets that are not related
Dots are scattered and do not appear to have a pattern or cluster

6. Causation vs. Association
Causation – when a change in one quantity causes a change in another
For example the number of loaves of bread and the amount of flour used.
This has a positive correlation. But the number of loaves of bread getting larger actually causes the amount of flour used to go up. So this is an example of causation.

7. Causation vs. Association
Causal relationships always have a correlation. However, two sets of data that a have a correlation may not have a causal relationship.
For example: the number of mailboxes and the number of firefighters in the city.
It is true the number of the mailboxes and firefighters will increase as the population increases. But installing more mailboxes does not CAUSE the number of firefighters to go up. There is only an association between the two.

8. Identify the correlation…
The number of empty seats in a classroom and the number of students seated in the class
The number of pets a person owns and the number of books that person read last year
The monthly rainfall and the depth of water in a reservoir
Negative Causation
No correlation
Positive Causation

9. What kind of correlation?
The number of umbrellas sold vs. the number of rainy days.
The number of minutes spent brushing your teeth vs. the number of cavities.
The number of people in this class vs. your bus number.
The average temperature in a city vs. the number of speeding tickets given in the city.
The number of people in an audience and ticket sales
The number of members in a family and the size of the family’s grocery bill
The number of times you sharpen your pencil and the length of your pencil

10. What kind of correlation? answers
The number of umbrellas sold vs. the number of rainy days. Positive Association
The number of minutes spent brushing your teeth vs. the number of cavities. Negative causation
The number of people in this class vs. your bus number. No correlation
The average temperature in a city vs. the number of speeding tickets given in the city. No correlation
The number of people in an audience and ticket sales. Positive causation
The number of members in a family and the size of the family’s grocery bill. Positive causation
The number of times you sharpen your pencil and the length of your pencil. Negative causation

11. Trend Line (Line of Best Fit)
Shows a correlation more clearly
Allows you to predict other related data
Makes it easy to determine a positive or negative correlation
Can be helpful when making predictions based on data.
Should be through the middle of the dots (same number of dots above the lines as are below the line)

12. Graphing a Scatter Plot from Given Data
The table shows the number of cookies in a jar from the time since they were baked. Graph a scatter plot using the given data.
Use the table to make ordered pairs for the scatter plot.
The x-value represents the time since the cookies were baked and the y-value represents the number of cookies left in the jar.
Plot the ordered pairs.

13. Interpolation – estimating a value between two values
Extrapolation – predicting a value outside of the range of known values.

14. Draw a trend line and use it to make a prediction.
Example
The scatter plot shows a relationship between the total amount of money collected at the concession stand and the total number of tickets sold at a movie theater. Based on this relationship, predict how much money will be collected at the concession stand when 150 tickets have been sold.
Draw a trend line and use it to make a prediction.
Draw a line that has about the same number of points above and below it. Your line may or may not go through some or all the data points.
Find the point on the line whose x-value is 150. The corresponding y-value is 750.
Based on the data, $750 is a reasonable prediction of how much money will be collected when 150 tickets have been sold. This is an extrapolation.

15. Another Example
Based on the trend line, predict how many wrapping paper rolls need to be sold to raise $500.
Find the point on the line whose
y-value is 500. The corresponding x-value is about 75.
Based on the data, about 75 wrapping paper rolls is a reasonable prediction of how many rolls need to be sold to raise $500. This is an interpolation.

17. Try these…
For Items 1 and 2, identify the correlation you would expect to see between each pair of data sets. Explain.
1. The outside temperature in the summer and the cost of the electric bill
Positive correlation; as the outside temperature increases, the electric bill increases because of the use of the air conditioner.
2. The price of a car and the number of passengers it seats
No correlation; a very expensive car could seat only 2 passengers.

18. Try these…
3. The scatter plot shows the number of orders placed for flowers before Valentine’s Day at one shop. Based on this relationship, predict the number of flower orders placed on February 12.
about 45