Lab Assignment on Regression Equations

Instructor: David Katz

 

In this lab, you will collect and organize data, and test for a correlation among the data. You may use the Statistical Abstract of the United States as your basic source material for tables of data. This book is available in the reference section of most libraries, or this reference is also available on-line at:

 

http://www.census.gov/prod/www/statistical-abstract-us.html

 

Or another good source of easy-to-collect data are tips if you or a friend work in the hospitality industry (e.g., restaurant, coffee shop, bar, etc.). Record the total tab from each customer and the corresponding tip for at least 10 different customers. Are your tips closer to 15% or 20%?

 

Make sure there is some possible or potential correlation between the data you choose. For example, avoid lists of data without any sensible correlation (e.g., heights in inches vs. social security numbers).

 

Steps To Complete This Lab:

 

  1. At the beginning of your lab, give the citation data (e.g., page number, original title, etc.). If you use the Statistical Abstract, give the table number and year of the edition.
  2. Select the columns and/or rows from the data you have chosen to serve as your lists of x-values and y-values. Make a two-column table of values to list your x-values and y-values. Label the quantity measured in each column.
  3. Graph the data using an x-y scatter plot. Label the quantity measured on the x-axis and the y-axis.
  4. Leave plenty of room to include captions for your two-column table and x-y graph. The captions should describe what is being measured in the table and the graph.
  5. Use your TI-83 or TI-84 calculator to compute the linear, quadratic, cubic, and quartic for your data. For each type of regression, write down the regression equation and the correlation coefficient r. You may round your answers to the hundredth place.
  6. Make a three-column table to summarize your regression results; use these column headings: Regression Type, Regression Equation, Correlation Coefficient. Decide which regression equation is the best-fit model of your data, and complete the following to use as the caption to this table, “The Best-Fit Regression Equation is the _____________” (chose between linear, quadratic, cubic, quartic).
  7. Graph the best-fit regression equation on the x-y scatter plot you made. Label the regression curve you draw on your graph.
  8. Choose an x-value that is not in your original set of data. This x-value should somewhere between the lowest and highest values in your data. Use the best-fit regression equation to predict the corresponding y-value. Show the arithmetic you do. Write a complete sentence to summarize your prediction. For example, “For an x-value of 72 inches, the best predicted y-value according to a quadratic regression model is 180 lbs.”, etc.
  9. What is the domain of your regression equation, or what is the smallest and largest x-value, you can input into your equation? Why? Explain in a complete sentence.

 

NOTE: many of the tables in the Statistical Abstract are very long and contain hundreds of items of data. You may select an abbreviated list of 10-15 data points for each scatter plot.

 

How You Are Graded (e.g., 48 out of 50 total points equals a grade of 96):

 

ITEM

POINTS

Citation or Copy of Article

5

Summarize your x and y-values in a table

5

Graph your x and y-values

5

Meaningful captions  on tables and graph 

5

Horizontal and vertical axes labeled on graph

5

Column headings on tables labeled

5

Select best-fit regression equation

5

Show arithmetic for predicted y-value

5

Write up prediction in complete sentence

5

Explain your domain

5

TOTAL POINTS

50

 

 

Typing the report is not necessary, but remember neatness counts! If I cannot read your report, I cannot grade it! Your finished report should be about 1-2 pages.

 

I encourage you to work together with your classmates to help write up the lab and/or find good articles with data tables. However, please don’t just copy verbatim a classmate’s lab report and hand it in as your own!

 

 

Return to Home Page