lesson 5-7 statistics: scatter plots and lines of fit
TRANSCRIPT
Lesson 5-7
Statistics: Scatter Plots and Lines of Fit
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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