1. Scatter Plots Standard: 806.5.3 Generalize the relationship between two sets of data using scatterplots and lines of best fit.

2. Vocabulary A scatter plot is a graph of a collection of ordered pairs (x,y) to show a relationship between two sets of data. A correlation describes the relationship between two sets of data. A line of best fit is a straight line that comes closest to the points on a scatter plot. You can use a line of best fit to help you make predictions from the data.

3. 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.

4. 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. Age12345678 Height2531343640414755

5. 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.

6. 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. Age of car 12345 Value$30,000$27,000$23,500$18,700$15,350

7. 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.

8. 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.

9. Constant Correlation The relationship is linear, but is neither positive, nor negative. Therefore, there is no correlation between the two.

10. Positive correlation: both data sets increase together. Negative correlation: as one data set increases, the other decreases. No correlation: changes in one data set do not affect the other data set. Strong vs. Weak Correlations

11. How do I draw a line of best fit? Imagine that the points enclose an area, then cut that area in half. If you use a ruler to draw the line you can move it around until you find a place where approximately half the points are on each side of the line. Increase your accuracy by drawing a shape around the area. Bisect the shape with your line.

12. How do I draw a line of best fit? The more linear the data, the narrower the area and the easier it is to draw the line.

13. Scatterplots Which scatterplots below show a linear trend? a) c)e) b) d)f) Negative Correlation Positive Correlation Constant Correlation

14. Year Sport Utility Vehicles (SUVs) Sales in U.S. Sales (in Millions) 1991 1992 1993 1994 1995 1996 1997 1998 1999 0.9 1.1 1.4 1.6 1.7 2.1 2.4 2.7 3.2 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 x y Year Vehicle Sales (Millions) 5432154321 Objective - To plot data points in the coordinate plane and interpret scatter plots.

15. 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 x y Year Vehicle Sales (Millions) 5432154321 Trend is increasing. Scatterplot - a coordinate graph of data points. Trend appears linear. Positive correlation. Predict the sales in 2001.

16. Plot the data on the graph such that homework time is on the y-axis and TV time is on the x-axis.. Student Time Spent Watching TV Time Spent on Homework Sam Jon Lara Darren Megan Pia Crystal 30 min. 45 min. 120 min. 240 min. 90 min. 150 min. 180 min. 150 min. 90 min. 30 min. 90 min.

17. Plot the data on the graph such that homework time is on the y-axis and TV time is on the x-axis. TVHomework 30 min. 45 min. 120 min. 240 min. 90 min. 150 min. 180 min. 150 min. 90 min. 30 min. 120 min. 90 min. Time Watching TV Time on Homework 30 90 150 210 60 120 180 240 240 210 180 150 120 90 60 30

18. Describe the relationship between time spent on homework and time spent watching TV. Time Watching TV Time on Homework 30 90 150 210 60 120 180 240 240 210 180 150 120 90 60 30 Trend is decreasing. Trend appears linear. Negative correlation.

19. 19 What have you learned so far?

20. Scatter Plots 9-9 Lesson Quiz: Part I Use the given information to make a scatter plot, and describe the correlation. Grading Period1234 Number of A’s56810 positive correlation

21. Scatter Plots 9-9 Identify a scatter plot for the given data. A. B. Lesson Quiz for Student Response Systems

22. Scatter Plots 9-9 Which scatterplot displays a negative relationship between the two variables?

23. Scatter Plots 9-9 Which type of relationship is best represented in the scatterplot below?

24. Scatter Plots 9-9 The ages and heights of a number of different plants of the same species are recorded on the scatterplot. Which equation represents a line of best fit for this scatterplot?

25. Scatter Plots 9-9 Which scatterplot displays a negative relationship over the entire set of data?