Question1Math 227 Project 1 Exploring relationships between two variabl

02 May Question1Math 227 Project 1 Exploring relationships between two variabl

Question
1

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 all of the x-values in your data, and put these in a separate column in your table.

g) Find the residuals. 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.

h) Put all the data (explanatory variable ????, response variable ????, predictions ?????, and residuals ????? − ????) in a separate table, and include it with your project.

http://www.city-data.com/

http://www.cde.ca.gov/ta/ac/ap/

http://graphics.latimes.com/responsivemap-pollution-burdens/

2

3. Draw Conclusions

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.

3

Math 227 Project 1 Exploring relationships between two variables -Score Sheet (Total 50 points)

Required Tasks Grading criteria Comments/Scores 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):

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) Find the residuals. Explain what it means when a residual is positive or negative. Identify and explain extreme residuals.

h) Put all the data (explanatory variable ????, response variable ????, predictions ?????, and residuals ????? − ????) in a separate table, and include it with your project.

2. Relevance and completeness of the analysis of the data including appropriate responses in step 2 Analyze the paired Data [25 pts]

4

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.

3. Completeness and appropriateness of drawing conclusions in step 3 Draw conclusions [10 pts]

4. Summarize Write a short summary of the main findings that

you discovered.

4. Clear summary of the main findings in step 4 Summarize [5 pts]

5. Overall quality of the report 5. Overall quality of the report and adherence of the project guidelines [5 pts]