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## Scatter Plots

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**4-7**Insert Lesson Title Here Scatter Plots Vocabulary scatter plot correlation line of best fit Course 3**4-7**Scatter Plots A scatter plot shows relationships between two sets of data. Course 3**4-7**Scatter Plots Additional Example 1: Making a Scatter Plot of a Data Set Use the given data to make a scatter plot of the weight and height of each member of a basketball team. The points on the scatter plot are (71, 170), (68, 160), (70, 175), (73, 180), and (74, 190). Course 3**4-7**Scatter Plots Correlation describes the type of relationship between two data sets. The line of best fitis the line that comes closest to all the points on a scatter plot. One way to estimate the line of best fit is to lay a ruler’s edge over the graph and adjust it until it looks closest to all the points. Course 3**4-7**Scatter Plots No correlation; as one data set increases, the other decreases. Negative correlation; as one data set increases, the other decreases. Positive correlation; both data sets increase together. Course 3**4-7**Scatter Plots Additional Example 2A: Identifying the Correlation of Data Do the data sets have a positive, a negative, or no correlation?. A. The size of a jar of baby food and the number of jars of baby food a baby will eat. Negative correlation: The more food in each jar, the fewer number of jars of baby food a baby will eat. Course 3**4-7**Scatter Plots Additional Example 2B: Identifying the Correlation of Data Do the data sets have a positive, a negative, or no correlation?. B. The speed of a runner and the number of races she wins. Positive correlation: The faster the runner, the more races she will win. Course 3**4-7**Scatter Plots Additional Example 2C: Identifying the Correlation of Data Do the data sets have a positive, a negative, or no correlation?. C. The size of a person and the number of fingers he has No correlation: A person generally has ten fingers regardless of their size. Course 3**4-7**Scatter Plots Try This: Example 2A Do the data sets have a positive, a negative, or no correlation?. A. The size of a car or truck and the number of miles per gallon of gasoline it can travel. Negative correlation: The larger the car or truck, the fewer miles per gallon of gasoline it can travel. Course 3**4-7**Scatter Plots Try This: Example 2C Do the data sets have a positive, a negative, or no correlation?. C. The number of telephones using the same phone number and the number of calls you receive. No correlation: No matter how many telephones you have using the same telephone number, the number of telephone calls received will be the same. Course 3**4-7**Scatter Plots Additional Example 3: Using a Scatter plot to Make Predictions Use the data to predict how much a worker will earn in tips in 10 hours. According to the graph, a worker will earn approximately $24 in tips in 10 hours. Course 3**4-7**Scatter Plots Try This: Example 3 Use the data to predict how many circuit boards a worker will assemble in 10 hours. 141210 8 6 4 2 Hours According to the graph, a worker will assemble approximately 10 circuit boards in 10 hours. 2 4 6 8 10 12 14 Circuit Board Assemblies Course 3**Scatter Plot**• A scatter plot is a graph of a collection of ordered pairs (x,y). • The graph looks like a bunch of dots, but some of the graphs are a general shape or move in a general direction.**Positive Correlation**• If the x-coordinates and the y-coordinates both increase, then it is POSITIVE CORRELATION. • This means that both are going up, and they are related.**Positive Correlation**• If you look at the age of a child and the child’s height, you will find that as the child gets older, the child gets taller. Because both are going up, it is positive correlation.**Negative Correlation**• If the x-coordinates and the y-coordinates have one increasing and one decreasing, then it is NEGATIVE CORRELATION. • This means that 1 is going up and 1 is going down, making a downhill graph. This means the two are related as opposites.**Negative Correlation**• If you look at the age of your family’s car and its value, you will find as the car gets older, the car is worth less. This is negative correlation.**No Correlation**• If there seems to be no pattern, and the points looked scattered, then it is no correlation. • This means the two are not related.**No Correlation**• If you look at the size shoe a baseball player wears, and their batting average, you will find that the shoe size does not make the player better or worse, then are not related.**Scatterplots**Which scatterplots below show a linear trend? a) c) e) Negative Correlation Positive Correlation b) d) f) Constant Correlation**Objective - To plot data points in the coordinate plane and**interpret scatter plots. y Sport Utility Vehicles (SUVs) Sales in U.S. 5 4 3 2 1 Year Sales (in Millions) 1991 0.9 1992 1.1 Vehicle Sales (Millions) 1993 1.4 1994 1.6 1995 1.7 1996 2.1 1997 2.4 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 x 1998 2.7 1999 3.2 Year**Scatterplot - a coordinate graph of data points.**y Trend appears linear. 5 4 3 2 1 Trend is increasing. Vehicle Sales (Millions) Positive correlation. Predict the sales in 2001. 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 x Year**Describe the relationship between time spent on**homework and time spent watching TV. Trend appears linear. 240 210 180 150 120 90 60 30 Trend is decreasing. Time on Homework 30 90 150 210 60 120 180 240 Negative correlation. Time Watching TV**Line of Best Fit**• A line of best fit is a line that best represents the data on a scatter plot. • A line of best fit may also be called a trend line since it shows us the trend of the data • The line may pass through some of the points, none of the points, or all of the points. • The purpose of the line of best fit is to show the overall trend or pattern in the data and to allow the reader to make predictions about future trends in the data.**1. Prepare a scatter plot of the data on graph paper.**Use the data to create a scatter plot**2. Using a straight edge, position it so that the plotted**points are as close to the line as possible. DRAW A LINE. 3. Find two points that you think will be on the "best-fit" line. Perhaps you chose the points (9, 260) and (30, 530). Different people may choose different points. All of them are "correct“.**4. Write the equation of the line.**5. This equation can now be used to predict information that was not plotted in the scatter plot. For example, you can use the equation to find the total calories based upon 22 grams of fat. If you have 22 grams of fat in your food, the it will also be about 427.141 calories.