Technology Exercise 2: Exploring Relationships Between Variables

Collecting the data

Go to the Box Office reviews at Yahoo Movies at You might want to right click and choose "Open in new window" so that you will still have these instructions available to you. We are going to gather information on the opening weekend movies, so make sure you don't collect your information during a weekend as the numbers are just estimates at that point and not complete.

We want the information for the Summer 2003 movie season, so we'll take movies from May 2, 2003, through August 31, 2003.

You can either use Excel and collect the data at home or Minitab and colect the information at school.

  1. Label the first four columns as "title", "date", "gross", and "theaters". That corresponds to the information about the movies that we'll be collecting.
  2. For each movie on the web page, look for those that have been in release for one week, ranked in the top 10 movies for that week, and had at least 2000 theaters. Enter the title, beginning date of the weekend (for example: August 8-10 would be entered as 08/08/03), the weekend gross in millions of dollars ($37,062,535 would get entered as 37.062535), and the number of theaters in the columns below the headings. Do not enter commas or dollar signs into any of the values.
  3. When you are done collecting information about this week, click on the pull down menu under "Archived Charts", select the previous week, and then click "GO". Enter the information for the new movies for that week and then repeat the process, choosing previous weeks until you can choose no more.
  4. The menu of archived weeks only allows for the last 12 weeks, but the previous weeks are available. The instructor has gone back and collected information for May and June so that you can still use that information. That table of information appears below these instructions. With luck, you might be able to cut and paste from this web page into your spreadsheet.
  5. Save your spreadsheet into the R: drive. Use the R:\xx\tech2 folder where xx is your section number (01, 02, or 03). Save it as a name that is unique for your group. If you are collecting this data at home, then save it onto a floppy disk to bring into school. If you feel comfortable making a folder to save your information into, then go ahead and save all your files in that folder.
title date gross theaters
Charlie's Angels: Full Throttle 6/27/2003 37.634221 3459
The Hulk 6/20/2003 62.128420 3660
Alex and Emma 6/20/2003 6.1110740 2310
Rugrats Go Wild! 6/13/2003 11.556869 3041
Hollywood Homicide 6/13/2003 11.112632 2840
Dumb and Dumberer 6/13/2003 10.845064 2609
2 Fast 2 Furious 6/06/2003 50.472480 3408
Finding Nemo 5/30/2003 70.251710 3374
The Italian Job 5/30/2003 19.457944 2633
Bruce Almighty 5/23/2003 85.734045 3483
The In-Laws 5/23/2003 9.222334 2652
The Matrix: Reloaded 5/16/2003 91.774413 3603
Daddy Day Care 5/09/2003 27.623580 3370
X2: X-Men United 5/02/2003 85.558731 3741
The Lizzie McGuire Movie 5/02/2003 17.338755 2825

Bringing the data into Minitab

We're now ready (finally) to bring the information into Minitab. This part is only necessary if you typed the information into Excel to start with. If you typed it into Minitab, then all you need to do is make sure you save the project into the proper location on the R: drive.

  1. Open the Excel spreadsheet by clicking on File and then Open Worksheet
  2. Change the "Files of type" to be Excel
  3. Navigate through the file system to find the location where you stored the Excel spreadsheet (for example, R:\01\tech2 or A: if you saved it on a floppy and brought it in from home).
  4. Highlight your file and click OK.
  5. Save your Minitab file onto the R: in the proper directory (see step 12 above) so that you can open it back up later. Go to File and choose Save Project As. Use a name that is unique to your group.

From now on, whenever you need to work with this data, open up your project by going to File and choosing Open Project.

For this project, the response variable (y) is the weekend opening gross sales (gross) and the predictor variable (x) is the number of theaters (theaters).

Making a scatter plot (Question 2)

Scatter plot of opening weekend sales vs number of theatersA scatter plot is appropriate when you have two quantitative (measurement level) variables and you want to see if they're correlated with each other.

  1. Choose Graph / Plot
  2. Click in the Y column for graph 1. Double click on the response variable (gross)
  3. Click in the X column for graph 1. Double click on the predictor variable (theaters)
  4. (Optional - Recommended) Add a title to the graph by choosing Annotation / Title
  5. Click OK

You may have more than one scatter plot on the same graph. If you do this, you probably want to use the same x variable for both, otherwise things can get really confusing.

You can also change the color of the dots (click on display item 1 and then edit attributes) or connect them (change symbol to connect, but that would be really ugly in this case).

Taking the Log (Question 3)

Fitted Line Plots

Scatter plot after taking log of gross salesBefore you decide to take the log of one of the variables, you might decide to play around with the graphs and see if it helps. We can use the Fitted Line Plot to do this. In this example, I'll take the log of the Y values.

  1. Choose Stat / Regression / Fitted Line Plot
  2. Enter the response and predictor variables in the appropriate blanks
  3. Click on Options (you probably don't want to take the log of both, it won't accomplish much).
    1. To take the log of the response variable (gross), check the Logten of Y and Display logscale for Y variable boxes.
    2. To take the log of the predictor variable (theaters), check the Logten of X and Display logscale for X variable boxes.
  4. (Optional - Recommended) Add a title. This is under the options button.

Notice how much more linear the data is now than it was before? That indicates that it is a good idea to take the log of the gross sales.

One caveat about taking the log of values. You can only find the logarithm of positive values. If you ever have negatives or even zero, you can't apply the logarithm transform. This means that you should never standardize and then take the log. If you're going to take the log, do it before you standardize the variables.

Transforming the Variable

If you have decided, like we did, that it would be good to transform both variables, then we need to calculate the new variable and save it so that we can use it in the future. In this example, we'll take the log of the gross sales for the opening weekend. If you decide that you would rather take the log of the number of theaters, then replace "gross" with "theaters" everywhere below.

  1. Label a blank column as log_gross
  2. Choose Calc / Calculator
  3. Store the results into log_gross
  4. The expression is "logt(gross)" without the quotes, obviously. Alternatively, you can scroll through the list of the functions to find "Log 10", double click on that, and then double click on gross.
  5. Click OK

Since we transformed the gross sales using the logarithm function, we need to make sure that we use log_gross from now on instead of gross. If you decide not to use the log transform, then continue to use gross instead of log_gross.

Find Descriptive Statistics (Question 4)

  1. Choose Stat / Basic Statistics / Descriptive Statistics
  2. Choose the variables log_gross and theaters.
  3. (Optional) Go into Graphs and choose Graphical Summary. This will give you all kinds of interesting information about the variables.
  4. Click OK

Find Regression Results (Question 5)

Finding Correlation

The regression results will give you a lot of information. Unfortunately, the one thing it doesn't give you is the value of the correlation coefficient. We'll find that first and then move on to regression.

  1. Choose Stat / Basic Statistics / Correlation
  2. Double click on the variables log_gross and theaters (the order doesn't matter).
  3. Click OK

The output will say "Pearson correlation of log_gross and theaters = X" where the number X is the correlation coefficient. It will also give you a p-value.

The p-value is the chance of getting the results we did if there is no linear correlation between our two variables. A small p-value (less than 5% or 0.05) means that our results are unlikely to happen if there is no correlation and so there must be linear correlation. A large p-value means that our results are likely to happen if there is no linear correlation and so it's likely that there's not any linear correlation.

Be sure to comment on the correlation in your project.

Finding Regression

  1. Choose Stat / Regression / Regression
  2. The response variable is log_gross. The predictor variable is theaters.
  3. (Optional - Required for Questions 6 and 7) Go into Storage. Check the boxes next to Residuals and Fits. Click OK.
  4. Click OK

There were two new variables that were created. RESI1 and FITS1. These are the residuals and the fits for this model. If you run this procedure again without unchecking Residuals and Fits, the variables will be called RESI2 and FITS2. The number will increment each time you re-run the regression procedure. Feel free to delete any unused columns by clicking on the column name (C6, C7, etc) and then hitting delete.

If this is the only residual and fits you have for your worksheet, you may want to relabel the columns as "residuals" and "fits". My examples will assume you've done this. If you don't do this, then use "RESI1" and "FITS1" instead.

Create an Annotated Scatter Plot (Question 6)

Scatter plot with centroid and means labeledYou did store the residuals and fits and relabel them in the last step, didn't you? If not, this question will be really difficult to do.

  1. Go to Graph / Plot
  2. For Graph 1, set the Y to log_gross and the X to theaters
  3. For Graph 2, set the Y to fits and the X to theaters. Minitab may complain about changes you made during question 2, go ahead and say it's okay.
  4. Under the Data Display, there are Items. Right now, only Item 1 has anything in it. We'll change that. Item 1 should display a Symbol for each Graph.
  5. Item 2 should be display a Connect for Each graph.
    1. To add this, click in the first box in the Item 2 row, then pull down the display menu and choose connect.
    2. Click in the second box in the Item 2 row, then pull down the for each menu and choose graph.
  6. Click on the Symbol for Item 1 and then Edit Attributes
    1. Graph 1 should have a solid black circle (change the color if you like, I changed mine to blue). Optionally change the point size to make them bigger (I made mine a 1.5)
    2. Graph 2 should have None for the type.
    3. click OK
  7. Click on the Connect for Item 2 and then Edit Attributes
    1. Graph 1 should have None for the type of line
    2. Graph 2 should have Solid for the type of line. Change the color and/or size if you want to (I made my size 3).
    3. Click OK
  8. Click on Frame / Multiple Graphs and then choose to overlay graphs on the same page.
  9. Click on Frame / Reference
    1. For item 1, type X in the direction field and the mean number of theaters in the position field. My mean (from question 4) for the theaters was 3071.3. Optionally change the line type to dashed and the color to red (or whatever color you like).
    2. For item 2, type Y in the direction field and the mean number of log_gross into the position field. The mean (from question 4) for the log of the gross was 1.3763. Optionally change the line type to dashed and the color to red (or whatever color you like).
  10. (Optional - Recommended) Add a title to the graph. Click on Annotation / Title
  11. Click OK. Make sure the graph looks right. If it doesn't fix it before going on to step 12. Changes made after this step are lost when you recreate the graph.
  12. To label the means on the graph, double click on the graph to go into edit mode. The Tools and Attributes toolbars will pop up.
    1. Choose the Text (big T in upper right) of the Tools toolbar.
    2. Click on the graph where you would like to add text
    3. Type "mean=1.3763" (except use your numbers) and click OK
    4. Now drag the text so that it is positioned where you want it.
    5. Repeat steps a) through d) with the mean of the theaters.
  13. On the toolbar at the top, there will be a little face with dots coming out of his eyes. Click that to go back into view mode. Alternatively, choose Editor / View from the menu system.

Whew! That involved a lot of steps. Make sure you get it right before you copy and paste it into Word.

Plotting the Residuals (Question 7)

residual plotsYou did generate the residuals and fits and then rename them back in question 5, right? Otherwise, this part will be difficult to do.

  1. Choose Stat / Regression / Residual Plots
  2. Use residuals (RESI1 if you didn't rename them) for the residuals and fits (FITS1 if you didn't rename them) for the fits.
  3. Click OK

Primarily we're interested in the normal probability plot (the residuals should be normally distributed) and the residuals vs fits graph (they should be fairly randomly scattered).

For the most part, they look good. There is that one outlier that opened in an average number of theaters but did poorly (Sinbad - you can tell by going back and finding that point in your data).

Fitted line plot of standardized variables (Question 8)

We talked about standardizing the variables on the first technology project and we've done a fitted line plot here, so there is nothing new here.

Standardizing the variables

  1. Label two empty columns as z_log_gross and z_theaters
  2. Go to Calc / Standardize
  3. Use log_gross and theaters for the input columns.
  4. Store the results in z_log_gross and z_theaters. Make sure the order is the same between the input and storage variables (that is, don't input log_gross and theaters but store into z_theaters and z_log_gross).
  5. Click OK

Fitted Line Plots

Fitted line plot of standardized variablesHey, we're almost done with this. You are remembering to think, show, and tell, right?

  1. Go to Stat / Regression / Fitted Line Plot
  2. Use z_log_gross for the response variable and z_theaters for the predictor variable.
  3. Go into Options and make sure that the Logten transforms are turned off (Minitab remembers that you had them turned on earlier).
  4. Go into Storage and make sure nothing is checked there.
  5. (Optional - Recommended) Put a title on the graph. This is in the options screen.
  6. Click OK
  7. Double click on the graph to go into edit mode (or use the menu and choose Editor / Edit)
  8. Choose the Text tool (the big T) and click somewhere close to the line in an empty space
    1. Type "slope = 0.877" (except use the value you found for the correlation coefficient in question 5) and click ok
    2. (Optional) Change the color and size of the text. Click once on the text to highlight. Click on the rainbow next to the ABC on the attribute toolbar and pick a color (I chose blue). Click on the two T's right below that to change the font size. The default is 1. I chose 1.25 to make it a little bigger.
    3. Drag the text so that it is viewable.
  9. Choose Editor / View from the menu system or click on the view icon on the toolbar (the face with the dots).

Even though you don't have to label the centroid on the graph, be sure to note how it's at (0,0) in your explanation of the graph.