GOALS/PROJECT OVERVIEW:  Collect and analyze “almost” linear data to determine and evaluate the accuracy of linear models. 

PARTNER AND DATA GUIDELINES:

1. PARTNERS:  You may work by yourself or with a maximum of two other students from any of the Algebra II Honors classes.  Only work in a group if you want to collaborate---NOT to delegate responsibilities!  Pick group members who you can meet up with after school or in a DR.  It is expected that you will meet and complete the project together.

2. DATA:  Collect a data set by conducting an experiment or research.  For an experiment, document the various steps of your procedure by taking pictures.  For research, gather all data from one source.

·        Your data set should be an area of interest for group members.  You will find this project much more enjoyable if you interested in the data and the results!

·        Your data set should be unique and creative.  I  have corrected over 300 of these projects and I want to see something different!

·        Your data set must exhibit a linear relationship.  Your “x” variable must be independent (such as time) and your data must be able to be ordered.

·        For research, your data set for regression must contain at least 10 points if you work alone and at least 15 points if you are in a group.  For experiments, 10 points is sufficient regardless of group size.  IMPORTANT:   You will also need at least two additional points for predictions so gather at least two extra values.

·        Once you have collected your data you should run a linear regression on the calculator and check your correlation coefficient.  If the “r” value does not suggest a somewhat strong (+ or −) correlation and/or the scatterplot does not look linear, start over and gather another data set or if possible you could zoom in on a particular piece of your data set that is more linear provided you will still have enough data points.  An r value between .6 and 1 or −.6 and −1 is acceptable.

·        In addition to your data set, you need at least two additional points that are used for predictions…these points are not part of your data set and are not used to determine the equation of the line of best fit!!!!  They should not be on your plot.

WHAT EACH GROUP MUST DO AND TURN IN: (Please submit in this order!)

1. One blank copy of the grading rubric on top with names filled in.

2. A copy of your data set fulfilling the specified requirements.  Identify variables.  Also identify the two prediction points that should be separate from your data set and should not be used in determining the equations of the line of best fit.  If your x is time it is best to rescale.  In other words, if data starts at 1990 then let x be years since 1990.

3. A paragraph describing how the data was collected. 

Ø      Why did you select your specific topic?

Ø      If you conducted an experiment then you must describe all the steps of your experiment in detail.  Your experiment description should read like those that you have seen in science class.  Pictures are great too!

Ø      If you conducted research then you must cite all your sources.  If your source is online then please submit a hardcopy printed from your source.

4. A scatterplot of your data without any lines of best fit drawn in.  Be sure to label both axes.  This can be done by hand on graph paper or using a computer (excel program).  You may want to photocopy your scatterplot so that you have a clean copy and a copy with the line of best fit sketched in.

5. Identify the algebraic line of best fit and include all work done to arrive at it.  Include another copy of your scatterplot with the algebraic line of best fit sketched and circle the two points used to determine the algebraic model’s equation.  In solving for “m” and “b”, you should use fractions in order to avoid approximating and losing accuracy.

6. Identify the calculator-generated equation for the line of best fit.  Again, don’t do too much rounding!  Use at least five decimal places.  Identify the correlation coefficient given by the calculator.

7. Use both of your equations (algebra and calculator generated) for the line of best fit to make at least two ‘predictions’ for the “y” coordinate by picking at least two values for “x” and finding the predicted “y” value.  Do not pick “x” values for which you can not test the accuracy of in step 8.  For example, if your x variable represents years since 1970 then you don’t want to pick x = 40 because that would be the year 2010 and we don’t know what actually happens in year 2010.  Use should use the “x” values that match those of your extra (non-data set) points.

8. Write several paragraphs evaluating the accuracy of both your algebraic model and your calculator model.  Which is the better model?  Be thorough!  This is a major part of your project and I expect lots of explanation and justification.  Here are just some of the things you should consider:

·        Compare model predictions to actual results. 

·        Consider/research outside factors (physical limitations, historical events...etc.) that may have impacted actual results. 

·        Significance of correlation coefficient. 

·        What does the slope and y-intercept represent in the context of your data and do these values seem reasonable?

9. Each member must completely answer the self-evaluation questions on his/her own.  This is the only piece of the group project that should not be consulted on.

DUE DATE:   All written work must be submitted prior to the close of school (2:15) on Monday 11/15 

Please see Mrs. Bachand with any questions

DATA PROJECT SELF EVALUATION:  EACH MEMBER SHOULD DO THIS PART ON HIS/HER OWN.  TYPE YOUR ANSWERS TO EACH OF THE FOLLOWING QUESTIONS.  PLEASE BE THOUGHTFUL AND USE COMPLETE SENTENCES!

1. List the responsibilities of each group member.

2. Do you feel that everyone did his/her fair share?

3. How much time do you estimate you spent on this project?

4. Please describe any difficulties that you had with project.

5. Why did you think this project was assigned?

6. Did you enjoy this project?  Why or why not?

7. Did you feel the directions were clear?  Any areas that need more clarification?

8. What advice would give a student who is just starting this project?

9. Looking at the rubric on the reverse side, how many points do you feel your project deserves?  Please justify your answer and do not fill in the rubric…that is for me to do!

Top Pieces of Advice from former students:

Name(s):  _________________________________________________________

DATA PROJECT RUBRIC

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