You will search for two quantitative variables that may have a linear correlation. You will describe and analyze the relationship between the variables.Math 227 Project 1 Exploring relationships between two variables
In this project, you will search two quantitative variables that may have a linear correlation. You will describe and
analyze the relationship between the variables the way it is explained in Chapter 4 (4.1-4.2). You will, then, create a
written report including all 4 parts below and turn in by the stated due date according to the guidelines provided in this
paper.
Required components:
1. Understand the Problem
a) Search for two quantitative variables that may have a linear correlation from the internet or any other media.
Possible websites to look for data:
•
•
•
•
You may obtain the data in StatCrunch.com: Click explore and click Data.
http://www.city-data.com/ for demographic information about cities
http://www.cde.ca.gov/ta/ac/ap/ for academic performance index.
http://graphics.latimes.com/responsivemap-pollution-burdens/ for pollution burdens.
Website where you found the data:
b) Use your intuition and/or experience to predict and write down the descriptions of the possible relationship:
Form, Direction, Strength, and outlier, etc.
c) Develop a question that address a possible linear correlation between two variables.
State the question(s):
Identify two variables from the data that are relevant to answer the questions:
2. Analyze the paired Data
a) What is the likely explanatory variable in the paired data?
b) Draw a scatter diagram of the data. Does the graph show a linear relationship between the variables?
Comment on the direction and strength appeared on the scatter diagram.
c) Compute the linear correlation coefficient between the two variables and interpret the meaning specifically
for your data. Use the list of critical values (see below) to determine whether you have enough data to make
any claims based on the coefficient obtained. If not, then you may want to consider collecting more data.
d) Find the least-squares regression line.
e) Interpret the slope and y-intercept, if appropriate.
f) Use the equation of the least-squares regression line to predict the outcome (y-value) for one of the x-values
in your data.
g) Find the residual for the x-value you chose in part (f). Explain what it means when a residual is positive or
negative. Identify cases with very high or very low residuals (dots that lie far away from the regression line) and
discuss why these may have such extreme residuals.
3. Draw Conclusions
1
a) What do the results indicate about the relationship between two variables?
b) Do you think there is a causal relation between the variables? Explain.
c) Relate the comments you made in step 1b before analyzing the data by commenting on both of the following:
How your expectation differs (or do not differ) from the actual results?
If it is relevant or meaningful in context, think of a way that these results could be used in practice.
4. Summarize
Write a short summary of the main findings that you discovered.
Grades will be based on:
1. Explanation of your topic and appropriate responses in step 1 Understanding the problem
[5 pts],
2. Relevance and completeness of the analysis of the data including appropriate responses in step 2 Analyze the
paired Data [25 pts],
3. Completeness and appropriateness of drawing conclusions in step 3 Draw conclusions [10 pts],
4. Clear summary of the main findings in step 4 Summarize [5 pts], and
5. Overall quality of the report and adherence of the project guidelines [5 pts].
Submission Guidelines and the due date:
The report including all graphs and symbols must be generated using computer and only the printed version will be
accepted. The report should contain the title, your name, date, course name and instructor’s name. The report should
not contain any misspelled words. The report will not be returned to you.
The printed project score sheet along with the title of your project and the website where you found your data (page 3-4
of this guidelines), must be submitted to the instructor by: ____________________
The project is due at the beginning of the lab on: ____________________
Note: Late submission will be accepted. However, there will be a 10% per day penalty from your final project grade.
Math 227 Project 2 Exploring relationships between two variables -Score Sheet (Total 50 points)
2
Name:________________________________________ Date:__________________________________
Title of the project: ____________________________________________________________________
Website where you found the data:_______________________________________________________
Project Grade: __________________________________
Required Tasks
1. Understand the Problem
a) Search for two quantitative variables that may
have a linear correlation from the internet or any
other media. (You may obtain the data in
StatCrunch.com. Click explore and click Data.)
Website where you found the data:
b) Use your intuition and/or experience to predict
and write down the descriptions of the possible
relationship: Form, Direction, Strength, and
outlier, etc.
c) Develop a question that address a possible linear
correlation between two variables.
State the question(s):
Grading criteria
1. Explanation of your topic and
appropriate responses in
step 1 Understanding the
problem [5 pts]
2. Analyze the paired Data
a) What is the likely explanatory variable in the
paired data?
b) Draw a scatter diagram of the data. Does the
graph show a linear relationship between the
variables? Comment on the direction and
strength appeared on the scatter diagram.
c) Compute the linear correlation coefficient
between the two variables and interpret the
meaning specifically for your data. Use the list of
critical values to determine whether you have
enough data to make any claims
d) Find the least-squares regression line.
e) Interpret the slope and y-intercept, if
appropriate.
f) Use the equation of the least-squares regression
line to predict the outcome ( ̂-value) for all of
the x-values in your data.
g) Use the equation of the least-squares regression
line to predict the outcome (y-value) for one of
the x-values in your data.
2. Relevance and completeness
of the analysis of the data
including appropriate
responses in step 2 Analyze
the paired Data [25 pts]
Comments/Scores
3
3. Draw Conclusions
a) What do the results you got indicate about the
relationship between two variables?
b) Do you think there is a causal relation between
the variables? Explain.
c) Relate the comments you made in step 1b before
analyzing the data by commenting on both of the
following:
How your expectation differs (or do not differ)
from the actual results? If it is relevant or
meaningful in context, think of a way that these
results could be used in practice.
4. Summarize
Write a short summary of the main findings that
you discovered.
3. Completeness and
appropriateness of drawing
conclusions in step 3 Draw
conclusions [10 pts]
5. Overall quality of the report
5. Overall quality of the report
and adherence of the
project guidelines [5 pts]
4. Clear summary of the main
findings in step 4 Summarize
[5 pts]
4
5
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