# Regression Analysis Project with Data

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```					A Linear Regression project for college students in a Statistics class

Tools and Concepts for Data Analysis
Final Project
Spring 2003
By
In this project students will use Tl-InterActive! to perform regression analysis on data to
develop a mathematical model that relates two variables. Then the students will use this
model to make predictions. Students should get into groups of two so that they can help
each other and discuss their findings with one another.

Objectives

•   find and use data directly from the Web.
•   extract data and copy it into a TI InterActive! document.
•   produce a scatter plot of the data
•   perform regression analysis to find the equation of the line that best fits the data
•   display the results, the plotted data and the regression equation together for visual
comparison
•   use the model to make predictions
•   make any conclusions about the data

Prerequisites

•   Students must have an introduction to TI InterActive! and must be able to extract data
from the internet, make a scatter plot and get the regression line prior to doing this
project.
•   Students must have a lesson on linear regression, must understand the concept of
correlation coefficient and the regression line.

Project Feedback

At the end of every presentation each team is being evaluated by the rest of the students
who fill out a project feedback form. This motivates students to do well and at the end
students learn from their mistakes.

Teacher notes

•   Sample of data printed on a spreadsheet
•   Scatter plot
•   Scatter plot wjth regression line
•   Linear regression results
Is the expression "if you shoot on goal you will score" true?
The game of hockey is based on passing the puck and shooting at the net. You often hear
that if you want to score, you have to shoot on goal. It seems like a logical assumption.
With this project you will try to verify if you can truly rely on that statement.

First you need data to support the argument. You will find this data on the Web at the
CBS site: http://cbs.sportsline.eom/u/hockey/nhl/stats/ and select scoring and insert data
in a list like the one below. You can choose statistics for any year. Make sure you state

Table of the number of shots on goal and goals for each team (Preseason stats from 2001)

Team               | Gls      |S
- -•
"New Jersey Devils"              29      215
"Detroit Red Wings"              26      300
"New York Rangers"              24!     208
"Boston Bruins"             24      221
"New York Islanders"              22      196
"Edmonton Oilers"              23|     216
"Phoenix Coyotes"              22j     185
"Ottawa Senators"              23      192
"Anaheim Mighty Ducks"              20      191
"Toronto Maple Leafs"              21      243
"Vancouver Canucks"              22      205
"Atlanta Thrashers"              23      204
"Washington Capitals"              19      179
"Minnesota Wi Id"            20 |    128
"Calgary Flames"             18      175
"Nashville Predators"              18      209
"Dallas Stars"!            17      162
"Los Angeles Kings"              18      163
"St. Louis Blues"              16!     115
"Pittsburgh Penguins"              18      159
"Tampa Bay Lightning"              15      148
"San Jose Sharks"             17      195
"Florida Panthers"              13!      166
"Chicago Blackhawks"              13|      196
"Carolina Hurricanes"              13i      174
"Buffalo Sabres"             14       174
"Columbus Blue Jackets"              15      217
1. pair with a classmate

2. select your data and extract data on a TI InterActive document. Make sure you and
your partner have different years' data or data from different teams. Make a copy of

3. make a scatter plot identifying the independent and dependent variables. Make a copy

4. perform regression analysis to find the correlation coefficient and the regression
equation. Make a copy of these results on a TI InterActive! document.

5. use the model to make any conclusions.

6. compare and discuss results with your partner.

7. write an essay explaining what you did, describe your data what were you hoping to
prove, any surprises, any conclusions

9. get feedback from your classmates by giving them a survey so that they can evaluate

Step 1 Select and extract your data

Start your TI InterActive! Click on the Web Browser and type in the CBS site:
http://cbs.sportsline.com/hockey/nhl/stats/ . Under SORT ABLE TEAM STATS select
Complete NHL, Scoring. Extract the data. Edit the lists so that you only keep the columns
of data that you need. Record the year of the statistics you'll be using for the project.

Step 2 Make a scatter plot

You need to verify the presence of a relationship between the two variables "shots" and
"goals". Make a scatter plot with these two variables. Show your independent and
dependent variables.

Step 3 Regression Analysis

Using TI InterActive! and the Stat Calculation Tool find the correlation coefficient, the
regression line and the regression equation. Show the scatter plot, the regression line, the
regression equation and the correlation coefficient.

Step 4 Make conclusions by answering the following questions

a) What does the correlation coefficient tell you? Is it positive or negative Why you
think?
b) Do you see a trend in your data? Explain.
c) What conclusions can you make with this information?
d) Is there sufficient evidence to conclude that there is a relationship between the
number of shots on goal and goals for each team?
e) If there is a relationship, how do we use it to determine how many goals a team will
have?
f) How many goals are expected from a team that has 200 shots?

Step 5 Compare results with your partner

a) Record your values for the correlation coefficient. How close or how far apart these
values are? Explain.
c) Using your regression equations and for a given value of shots do you both get the
same predicted number of goals ?Explain.
Write an essay explaining what you did, describe your data what were you hoping to
prove, any surprises, any conclusions.

Step? Evaluation

After your presentation give your classmate the attached Project Feedback and give them
the chance to evaluate your work. Review the scoring and think what if anything you
should have done better.

Step SCheck list

Use the following check list to make sure you have everything before you submit your
project.

Data table
Scatter plot
Scatter plot with regression line
Regression equation and correlation coefficient
Essay
Project feedback forms
Project Feedback

Beginner          Developing       Accomplished      Exemplary       Score
1 point           2 points         3 points          4 points
Cooperative   Did not work at   Worked well      Worked well       Worked
group work    all no            some of the      most of the       well all of
communication     time, some       time and          the time ,
communicatio     communicated      communica
n with           with partner      ted with
partner                            partner at
all times
and shared
information

Gathered      Did not collect   Collected        Collected some    Collected a
information   any               very little      basic             great deal
information       information -    information -     of
that relates to   some relates     most relates to   information
the topic         to the topic     the topic.        - all relates
to the topic

given         attempted.        completed        completely        completed.
questions     Directions not    partially,       finished          Explanation
followed, many    directions not   according to      s well
errors and poor   completely       directions.       thought out
effort            followed,        Minor errors,     and clearly
demonstrated      explanations     explanations      explained
unclear and      somewhat          and
minimal          unclear and       excellent
effort           average effort    effort
demonstrated     demonstrated      demonstrat
ed

Completing    Steps             Steps            Steps             Steps
every step    attempted.        completed        completely        completed.
Directions not    partially,       finished          Explanation
followed, many    directions not   according to      s well
errors and poor   completely       directions.       thought out
effort            followed,        Minor errors,     and clearly
demonstrated      explanations     explanations      explained
unclear and      somewhat          and
minimal          unclear and       excellent
effort           average effort    effort
demonstrated     demonstrated      demonstrat
ed
Presentation   The volume,       The volume       The volume        The
to class       clarity and       and clarity of   and clarity and   volume,
organization of   the              organization of   clarity and
the               presentation     the               organizatio
presentation is   is good and      presentation is   n of the
poor              shows            very good         presentatio
evidence of                        n is
organization                       excellent
and it
engages
the
students

Maximum number of points is 20

Teacher Notes
Team                 GlS        S
"New Jersey Devils"              29       215
"Detroit Red Wings"              26       300
"Newt York Rangers"            24       208
"Boston Bruins"            24       221
"Newi York Islanders"             22       196
"Edmonton Oilers"             23       216
"Phoenix Coyotes"             22       185
"Ottawa Senators"             23       192
"Anaheim Mighty Ducks"              20       191
"Toronto Maple Leafs"              21       243
"Vancouver Canucks"              22       205
"Atlanta Thrashers"              23       204
"Washington Capitals"              19       179
"Minnesota Wild"            20       128
"Calgary Flames"            18       175
"Nashville Predators"              18       209
"Dallas Stars"            17       162
"Los Angeles Kings"              18       163
"St. Louis Blues"             16       115
"Pittsburgh Penguins"              18       159
"Tampa Bay Lightning"              15       148
"San Jose Sharks"             17       195
"Florida Panthers"             13       166
"Chicago Blackhawks"              13       196
"Carolina Hurricanes"              13       174
"Buffalo Sabres"            14       174
"Columbus Blue Jackets"              15       217

Now ,you need to verify the presence of a relationship between the two variables "shots"
and "goals". First, you need to make a scatter plot' with these two variables.
Scatter plot

80

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100 200 300 400 500 600 700

Linear Regression Results

shots vs goals
Linear Regression (a+bx)
regEQ(x) = -3.21852 + .0958692x
a = -3.21852
b = .0958692
r = . 951091
Scatter plot

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70

60

50

40

30

20

10

100 200 300 400 500 600 700

Linear Regression Results

shots
Linear Regression (a+bx)
regEQ(x) = -3.21852 + .0958692x
a = -3.21852
b=.0958692
r = .951091

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