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Grade 9:  The Learning Equation Math

41.03 Correlation of Data

4icon.gif (5323 bytes)

Data Analysis

Refresher pp 98-9

 

 

SeekAWord2ech.class Author

Prerequisite Skills:

 

Key Terms                 

scatter plot, trend, line of best fit (trend line), independent variable, dependent variable, discreet variable, continuous variable, positive correlation, negative correlationweak correlation, strong correlation

 

 

Learning Outcomes:

The student will:

Line of Best Fit

correlation_ani.gif (101316 bytes)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
up and right
0.7 to 1.0 0.3 to 0.7
Negative
down and left
-1.0 to -0.7 -0.7 to -0.3

Little or No Correlation:  -0.3 to 0.3

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 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.
    • Click "Enter"in either cell of the last row if you wish to add additional data.
    • Click on "Update Display" to plot the points.  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 critical to this lesson.  It is useful, however to help us understand the strength of data correlations.

  • 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

 

Positive Trend

positive trend (correlation) - both sets of data increase together

Perfect Positive Trend (Correlation)

corr1.gif (1115 bytes)

source:  Correlation

 

Olympic Gold Medal Winning High Jump (1900 - 1984)

scatterplot1.gif (2306 bytes)

source:  quizregsol.html

 

1993 Chicago Bulls Basketball

bulls93.gif (5783 bytes)

Negative Trend

negative trend (correlation) - one set of data decreases as the other set of data increases

Strong Negative Trend (Correlation)

scatterplot-.gif (3053 bytes)

 

Weak Negative Trend (Correlation)

corr2.gif (1252 bytes)

source:  Correlation

 

No Trend (Correlation)

corr0.gif (1639 bytes)

source:  Correlation

 

Correlation Strength

  • The correlation coefficent ranges between -1 and 1.  It is part of the 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

  • Move the slider on the applet below to see the data points move from a strong negative correlation on the far left to no correlation in the middle, and a strong positive correlation on the far right.

Linked to applet at:  http://www.seeingstatistics.com/seeing1999/gallery/CorrelationPicture.html

 

Study the following results:
graph8.jpg (15798 bytes)
source:  The New Utilities

In this experiment:

  • what are the dependent and independent variables?
  • are the variables continuous or discrete?
  • is the relationship between the dependent and independent variables linear or non-linear?
  • what trend is illustrated?

answers.gif (2302 bytes)

 Click Reload Page between answers selections.

 

 

linegraph1.gif (15526 bytes)

source:  bios150WMU

In this experiment:

  • what are the dependent and independent variables?
  • are the variables continuous or discrete?
  • is the relationship between the dependent and independent variables linear or non-linear?
  • what trend is illustrated?

answers.gif (2302 bytes)

 Click Reload Page between answers selections.

 

 

linegraph2.gif (16880 bytes)

source:  Welcome to the Line Graph page!

In this experiment:

  • what are the dependent and independent variables?
  • are the variables continuous or discrete?
  • is the relationship between the dependent and independent variables linear or non-linear?
  • what trend is illustrated?

answers.gif (2302 bytes)

 Click Reload Page between answers selections.

 

Review:

PlotHow - Scatterplots

 

Enrichment:

Webstat Directions: 

These directions were included in an earlier lesson.   Look at all 4 steps before you start.  When you click on the button below, Webstat will open.

Choose a Sample data stet..  CEO salaries is an interesting set of data.

webstat4.gif (63308 bytes)

Choose one of the graph types from Graphics.  

scatterplot4.gif (22830 bytes)

Choose your Age and Salary for your variables, then click Create Graph!

scatterplot3.gif (14218 bytes)

Try a variety of data Sample data sets and graphics(graph types).  For each data try to answer:
  • what are the dependent and independent variables?
  • are the variables continuous or discrete?
  • is the relationship between the dependent and independent variables linear or non-linear?
  • what trend is illustrated?

Scatterplot and Correlation Coefficient

Correlation and Regression

 

 

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