Lesson 5-7

Statistics: Scatter Plots and Lines of Fit

Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.

Objectives

• Interpret points on a scatter plot

• Write equations for lines of fit

Vocabulary

• Scatter plot – Two sets of data plotted as ordered pairs in a coordinate plane

• Positive correlation – in a scatter plot, as x increases, y increases

• line of fit – a line that describes the trend of the data in a scatter plot

• Best-fit line – The line that most closely approximates the data in a scatter plot

• Linear interpolation – The use of a linear equation to predict values that are inside of the data range

• Negative correlation – in a scatter plot, as x increases, y decreases

y

x

y

x

x-y Coordinate Plane

Quadrants

III

III IV

Point Plotting

(x, y) (-4, 7) (5, -8)

x – left or righty – up or down

right 5

down 8

left 4

up 7

Example 1a

Determine whether the graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it.

The graph shows average personal income for U.S. citizens.

Answer: The graph shows a positive correlation. With each year, the average personal income rose.

Example 1b

The graph shows the average students per computer in U.S. public schools.

Answer: The graph shows a negative correlation. With each year, more computers are in the schools, making the students per computer rate smaller.

Determine whether the graph shows a positive correlation, a negative correlation, no correlation. If there is a positive or negative correlation, describe it.

Example 2a

The table shows the world population growing at a rapid rate.

Year Population (millions)

1650 500

1850 1000

1930 2000

1975 4000

1998 5900

Draw a scatter plot and determine what relationship exists, if any, in the data and draw a line of fit.

Example 2a cont

Let the independentvariable x be the yearand let the dependentvariable y be thepopulation (in millions).

The scatter plot seems to indicate that as the year increases, the population increases. There is a positive correlation between the two variables.

Draw a line of fit for the scatter plot.

No one line will pass through all of the data points. Draw a line that passes close to the points. A line is shown in the scatter plot.

Example 2b

Write the slope-intercept form of an equation for equation for the line of fit.

The line of fit shown passes through the data points (1850, 1000) and (1998, 5900).

Step 1 Find the slope.

Slope formula

Letand

Simplify.

Example 2b cont

Step 2 Use m = 33.1 and either the point-slope form or the slope-intercept form to write the equation.You can use either data point. We chose (1850, 1000).

Point-slope form Slope-intercept form

Answer: The equation of the line is .

Example 3

Use the prediction equation y ≈ 33.1x – 60,235 where x is the year and y is the population (in millions), to predict the world population in 2010.

Original equation

Replace x with 2010.

Simplify.

Answer: 6,296,000,000

Summary & Homework

• Summary:– If y increases as x increases, then there is a

positive correlation between x and y– If y decreases as x increases, then there is a

negative correlation between x and y– If there is no relation between x and y, then there is

no correlation between x and y– A line of fit describes the trend of data– You can use the equation of a line of the fit to

make predictions about the data

• Homework: – N/A