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Grade 9:  The Learning Equation Math

41.04 Line of Best Fit

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Data Analysis

Refresher pp 100-1

 

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Prerequisite Skills:

Correlation of Data

 

Key Terms                 

line of best fit, range, interpolate, extrapolate, lower extreme, upper extreme, trend, independent variable, dependent variable, discreet variable, continuous variable, positive correlation, negative correlation, weak correlation, strong correlation

 

Interactive Component Under Construction

 

 

Learning Outcomes:

The student will:

line of best fit (trend line) - A line on a scatter plot which can be drawn near the points to more clearly show the trend between two sets of data.  The data is used to derive a curve of best fit.

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Line of Best Fit

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The correlation coefficent (r) ranges between -1 and 1.  It is part of the following applet, but will not critical to this lesson. It is useful, however to help us understand the strength of data correlations.

Correlation Strong Weak
Positive 0.7 to 1.0 0.3 to 0.7
Negative -1.0 to -0.7 -0.7 to -0.3

Little or No Correlation:  -0.3 to 0.3

Line of Best Fit

Add up to 50 points onto the green viewing screen by clicking on the screen with the mouse, a red line represents a line passing through (Average x, Average y).  The slope of the red line can be altered by clicking the Left or Right buttons on the "Rotation Scroll Bar".  By clicking on Show Best Fit, a  blue best fit line will also appear.

The slope of red line may be changed by dragging the mouse either right or left.

The thermometer on the right measures how well the red line fits the data points. If the thermometer measures a good fit (that is, small error) then the red line is a good fit to the data..

 

Applet Source, Written by Nicholas Exner

download source:  Java Applets and Activities

 

Directions:  Use the following to examine 3 scatterplot samples and to create your own scatterplots.
  • Click the "Load Data File" button to see the first scatterplot sample.   The other two samples are available from the pulldown menu.  To display the sample, click the "Load Data File" button after selecting a sample. Click on various spreadsheet cells and change the values.  Notice the effect the change has on the line of best fit.
  • Create your own scatterplots by entering the data points into the spreadsheet to the left of the graph.
    • The slope and intercept of the line of best fit is given, but will not be emphasized in this lesson.

source:  http://math.hws.edu/javamath/config_applets/index.html

Directions:  Use the following to examine 3 scatterplot samples and to create your own scatterplots.
  • Click the "Load Data File" button to see the first scatterplot sample.   The other two samples are available from the pulldown menu.  To display the sample, click the "Load Data File" button after selecting a sample. Click on various spreadsheet cells and change the values.  Notice the effect the change has on the line of best fit.
  • Create your own scatterplots by entering the data points into the spreadsheet to the left of the graph.
    • The correlation coefficent ranges between -1 and 1.  It is part of the applet, but will not be emphasized in this lesson.
    • The slope and intercept of the line of best fit is given, but will not be emphasized in this lesson.
  • To interpolate, plot the point on the line between the outer most points on the curve.

  • To  extrapolate, plot the point on curve of best fit outside of the other points on the curve.

source:  http://math.hws.edu/javamath/config_applets/index.html

 

Review:

Enrichment:

 

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