Scatter Plots

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

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

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

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

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.

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.

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

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

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

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)

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.

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

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.

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.

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.

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