REGRESSIONS

Graphical Analysis
MS Excel
TI-83

GRAPHICAL ANALYSIS

Graphical Analysis 3.x is produced by Vernier Software and Technology in Beaverton, OR. It is available for both Macintosh and PC. This program conducts analysis exceedingly well. The process is very similar to using Excel, except the graph is automatically built for you as you enter the data.
  1. Enter the data in the columns provided. Place the Control Variable in the left column and the Dependent Variable in the right column.
  1. The graph has automatically been drawn for you. Click on the title bar of the graph to make sure it is selected rather than the data. On Macintosh, clear strips will run across the title bar. On PC's, the border of the graph will darken.
  1. Under Analyze, select Curve Fit.
  1. From the menu that is presented, select Power.
  1. When you click on Try Fit, the small copy of your graph will get a black line on it showing the curve for the power fit. This is shown here.
  1. When you click OK, the full graph is redrawn with the curve placed over the data points and the equation displayed in a box that floats above the graph.
 
  1. The equation for our data is: distance = 2.05 * time1.98. With 1.98 being essentially 2.00, we reach the conclusion that the relationship is probably a squared one or ...

d a t2

NOTE: Using a Power Regression requires that none of the data points be zero. A zero value will return an ERROR message, whether it is a computer program or a graphing calculator. If you have the origin as one of your data points, just delete it from your data set.

  1. We cam test the relationship further by plotting a graph of d vs. t2 on top of the data points. If there's a good fit, it assures us that we have concluded correctly. Click the results of our power analysis away by clicking on the small square at the upper left-hand side. You may have to click the box once to select it. Go back to Analyze - Curve Fit, but this time select Quadratic. Click Try It, then OK. You should get the final result shown here, which is good evidence that this is definitely a square relationship, or distance is proportional to the time squared.

Microsoft Excel

Excel can be used to good advantage in the analysis of experimental data that is of the form we have been studying in this web site. The version used here is from Office 98 for Macintosh, and is essentially the same as Office 87 for PC. Other versions on either side of this behave very similarly.

The steps needed to use Excel are:

  1. Enter the data in columns as you would in a normal data table. Place the Control Variable in the left column and the Dependent Variable in the right column.
  1. Select the two columns of data by clicking and dragging over the data table.
  1. Choose Graph Wizard from the menu bar. The icon may vary from one version of Excel to another.
  2. Select scatter graph as your style, and label the axes.
  1. Now that you have a finished graph, you want to add a trend line and statistics. Double click on one of the data points in the graph. All of the points should become highlighted as shown here.
  1. Then find the menu item to Add Trendline.
  2. Choose Power. Be sure to click "Display equation" under Options.
  1. The result is a regression line through the data points, and the resulting equation displayed on the graph.
  1. In this case, the equation is given as:
  1. This says that the distance is 2.07 times the time raised to the 1.97 power, which is almost 2. Given a small amount of latitude for lab data, we conclude that the form of the relationship is a square one, or
    d a t2

    NOTE: Using a Power Regression requires that none of the data points be zero. A zero value will return an ERROR message, whether it is a computer program or a graphing calculator. If you have the origin as one of your data points, just delete it from your data set.

TI-83 GRAPHING CALCULATOR

While there are various ways to enter data into a graphing calculator, we often choose the simplest one. Data that is entered via a CBL2 or LabPro will automatically be included in the lists. The only challenge is determining which list contains which set of values.

Manually enter the data in the lists of the TI-83+:

  1. Press [STAT] then [ENTER] (with "EDIT" highlighted).
  2. If the lists L1 and L2 contain numbers, you can clear them by successive presses of the delete key [DEL], or you can use the up-arrow to move the cursor to the very top of the list where the label is. Now press [CLEAR] then [ENTER] and the entire list will be erased.
  3. The first list, L1, will represent time in seconds. The second list, L2, will represent distance in cm.
  4. Type the first number, 1.00. It appears at the bottom of the screen. Pressing [ENTER] puts it in the list and moves the cursor down one row. Continue entering data until your lists resemble the diagram below.
  5. Leave the lists area by pressing [2nd] [QUIT].

Display the graph:

  1. Note: You don't need to leave the lists area to initiate this step.
  2. Press [GRAPH]. You should see a graph resembling the one below. If you don't, press the [ZOOM] button followed by [9] to autoscale the graph to fit the screen.
  3. Examine the graph. It has the general characteristics of a quadratic but you can't really be sure. Now it's time to use the power of your handheld computer.

Determine the equation:

  1. Press [STAT] again, but this time use the right-arrow to highlight "CALC". This will allow you to explore the nature of the relationship further. A list of types of analyses is presented to you.
  2. The relationships we have worked most with are in a class called "power" relationships. All are of the form y = kxn where the power 'n' can have almost any value. As you look down the list, you don't see "PwrReg" as you expect. If you use the down-arrow to scroll down, you find other types below #7, so you keep going. At A, you find "PwrReg". Stop there.
  3. Press [ENTER] to calculate the regression. You go back to the home screen at this point, and need to press [ENTER] once more to activate the process.
  4. Your results should resemble the following:
  5. From this information, we determine that our data is best represented by the equation:
    Distance = 2.07 * Time    1.97 , with distance in m, time in sec.
  6. The value 1.97 is very close to 2.0, indicating that this data belongs to a quadratic relationship, or
d a t2

NOTE: Using a Power Regression requires that none of the data points be zero. A zero value will return a DOMAIN error message. Also, your lists must be identical in length. An extra or missing value in either list will result in a DIM MISMATCH error.

If you do not get the values for r2 and r as shown above, you can turn the regression statistics on by going through this short sequence. It shouldn't need to be repeated unless the battery runs out.

The next time you do a regression, the regression values will be displayed.

What does the "r" value mean? The closer the value of "r" is to 1.000, the more closely the data fits the equation you are given perfectly. This is a statistical value, and give you confidence (or the opposite) that the result you will report has validity.

 
Written August 2001
Updated October 2003