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Purpose of a Scatter Plot

1. The purpose of a scatter plot is to show the type of relationship, or correlation, that exists between two sets of data.
a. For instance, a positive correlation means that as the value of one set of data increases, the other data will also increase. An example of a "positive correlation" is the amount of rain and the size of puddles. Obviously, the more it rains, the larger the size of the puddles. In a scatter plot, "positive correlation" could look like this:
  illustration of a scatter plot
  b. There is a different type of relationship between the life of a watch and its battery. This specific example shows a "negative correlation" because the more the watch is in use, the less energy is left in its battery. In a scatter plot, "negative correlation" could look like this:
  illustration of a scatter plot
  c. Lastly, there may be two sets of data that has "no correlation". In this relationship, the value of one set of data has neither "positive" nor "negative" effect on the other set of data. Imagine yourself drinking a glass of water. Do you now feel like doing more or less homework? Your answer to this question at that time would have nothing to do with drinking more water. This is because there is "no correlation" between how much water you drink and how much homework you do. In a scatter plot, "no correlation" could look like this:
  illustration of a scatter plot


Drawing a Line of Best Fit

2. If the scatter plot shows that the relationship between two sets of data has a positive or negative correlation, another use for the scatter plot is to be able to make predictions using a "line of best fit" or "fitted line". The line of best fit allows you to make predictions because every point on the line is associated with a glide slope value and average speed value. Thus, any value I choose for glide slope will have a corresponding average speed value, which can be found by locating the point on the line of best fit.
  Here are the steps for drawing the line of best fit:
  a. Be sure a positive or negative correlation exists.
b. Using a ruler, draw a line of best fit. You must use a ruler!
  The line of best fit is an approximation. There isn't just one correct answer for drawing the line. Not everyone's line of best fit will be exactly the same. To draw a more accurate line, imagine the points are cities on a map and you want to be able to drive as close as you can to each city on one, straight road. Using a ruler, draw one, straight road that would take you as close as possible to every city. It is okay if your line goes through a city, and it is also okay if your line doesn't touch any of the cities. The goal is not to go through all the cities, so do not connect the dots. The goal is to get close to all the cities, using one, straight road.
  One technique you can use to draw the line is to hold the ruler on it's side and pretend it is the road you want to draw. Place it somewhere in the cities and look on either side of the road to make sure that it comes as close to all the cities as possible. You can move the road, simply by moving the ruler. Once you've found the perfect spot for your road, carefully mark the top and bottom of the ruler with a dot and draw your line.
c. Draw the line so that it goes as far left and as far right as possible without drawing the line through the axes and without drawing the line passed the axes lines.
d. Practice drawing a line of best fit in each of the scatter plots below:
  worksheet for scatter plot practice

Answer Key



Using the Line of Best Fit for Making Predictions

3. Here are the steps for using the line of best fit for making predictions
a. Choose a glide slope value from the x-axis.
  b. Hold your ruler vertically (parallel to the sides of your paper) to find the point on the line of best fit that is exactly above the glide slope value you selected from the x-axis. Mark that point.
  c. Hold your ruler horizontally (parallel to the bottom of your paper) and line it up with the mark you made on the line of best fit to find the point on the y-axis. Mark that point.
  d. Determine the value of the speed.
  e. This value is an educated approximation of the average speed of the glider according to the glide slope.
  f. The same procedure can be done in reverse to find the approximation of the glide slope if you choose an average speed value from the y-axis.
  g. Practice making predictions by using the scatter plots below:
#1: If glide slope value = 20 degrees
Then, average speed = ________ in/sec

worksheet for practice

#2: If glide slope value = 30 degrees
Then, average speed = ________ in/sec

worksheet for practice

#3: If average speed = 15 in/sec
Then, glide slope = ________ degrees

worksheet for practice

#4: If average speed = 25 in/sec
Then, glide slope = ________ degrees

worksheet for practice

Answer Key



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