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

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.

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

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

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

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

y x THE COORDINATE PLANE ( 1 , 3 ) 5 4 3 2 1 -1 -2 -3 -4 -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. x -5 -4 -3 -2 -1 1 2 3 4 5 The FIRST number is called the X- coordinate. ( 1 , 3 ) The SECOND number is called the Y- coordinate.

Ordered pair to graph (x, y) 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) 27 (6, 27)

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

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.

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

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.

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

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.

Which scatterplots below show a linear trend? 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 1998 2.7 1991 1993 1995 1997 1999 1992 1994 1996 1998 2000 x 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

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

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 240 210 180 150 120 90 60 30 30 min. 180 min. 45 min. 150 min. 120 min. 90 min. Homework Time on 240 min. 30 min. 90 min. 120 min. 150 min. 120 min. 180 min. 90 min. 30 90 150 210 60 120 180 240 Time Watching TV

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. Homework Time on 30 90 150 210 60 120 180 240 Negative correlation. Time Watching TV