# Lesson 11.4 - Scatter Plots  Learn how to construct a scatter plot and analyze the relationship between two variables according to M7D1f, M7A3a and c standards on the coordinate plane with the y-axis representing one variable.

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1. Lesson 11.4: Scatter Plots Lesson 11.4: Scatter Plots Standards: M7D1f & M7A3a & c Objective: To construct a scatter plot and determine the relationship between two variables.

2. Scatter Plot Scatter Plot • A scatter plot is a graph of plotted points that shows if there is a relationship between two sets of data or two variables. • The graph looks like a bunch of dots, but some of the graphs have a general shape or move in a general direction.

3. y This vertical line is called the y-axis. THE COORDINATE PLANE THE COORDINATE PLANE

4. This horizontal line is called the x-axis. y x -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4 5 5 5 5 4 4 3 3 2 2 1 1 0 0 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 THE COORDINATE PLANE THE COORDINATE PLANE

5. y x -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4 5 5 5 5 4 4 3 3 2 2 1 1 0 0 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 The x-axis and y-axis separate the coordinate plane into 4 parts. origin This point in the middle of the x-axis and y-axis is called the origin . THE COORDINATE PLANE THE COORDINATE PLANE

6. THE COORDINATE PLANE THE COORDINATE PLANE y x Quadrant II -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4 5 5 5 5 4 4 3 3 2 2 1 1 0 0 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 Quadrant I Quadrant III These parts are called Quadrants. Quadrant IV

7. y x -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4 5 5 5 5 4 4 3 3 2 2 1 1 0 0 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 To locate a point anywhere on the grid, you need an ordered pair. An ordered pair is a pair of numbers used to locate points on a grid. ( 1 , 3 ) The FIRST number is called the X- coordinate. THE COORDINATE PLANE THE COORDINATE PLANE The SECOND number is called the Y- coordinate.

8. Construct a scatter plot to show the relationship between the hours spent practicing shooting darts and the dart shooting score. Practice Time (hours) Dart Shooting Score Ordered pair to graph (x, y) 1 6 (1, 6) 2 8 (2, 8) 3 13 (3, 13) 4 20 (4, 20) 5 18 (5, 18) 6 27 (6, 27)

9. Construct a scatter plot to show the relationship between the hours spent practicing shooting darts and the dart shooting score. 0 5 10 15 20 25 30 0 1 2 3 4 5 6 Practice Time (hrs) Dart Shooting Score Practice Time versus Dart Shooting Time Ordered pair to graph (x, y) (1, 6) (2, 8) (3, 13) (4, 20) (5, 18) (6, 27)

10. Positive Correlation Positive Correlation • If the x-coordinates and the y-coordinates both increase, then the two variables are said to have a POSITIVE CORRELATION. • This means that both are going up, and they are related.

11. Positive Correlation 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. • Can you think of any other examples of variables with a positive relationship? Age 1 2 3 4 5 6 7 8 Height “ 25 31 34 36 40 41 47 55

12. Negative Correlation Negative Correlation • If the x-coordinates and the y- coordinates have one increasing and one decreasing, then the two variables are said to have a 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.

13. Negative Correlation 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. • Can you think of anything else with a negative relationship? Age of car 1 2 3 4 5 Value \$30,000 \$27,000 \$23,500 \$18,700 \$15,350

14. No 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.

15. No Correlation 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.

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

17. 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) 5 4 3 2 1 Objective - To plot data points in the coordinate plane and interpret scatter plots.

18. 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 x y Year Vehicle Sales (Millions) 5 4 3 2 1 Trend is increasing. Scatterplot - a coordinate graph of data points. Trend appears linear. Positive correlation. Predict the sales in 2001.

19. 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. 180 min. 150 min. 90 min. 30 min. 90 min. 90 min. 90 min.

20. Plot the data on the graph such that homework time is on the y-axis and TV time is on the x-axis. TV Homework 30 min. 45 min. 120 min. 240 min. 90 min. 150 min. 180 min. 180 min. 150 min. 90 min. 30 min. 120 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

21. 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.