Question:

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, cre

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.

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 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 2 Exploring relationships between two variables -Score Sheet

(Total 50 points)

Name:________________________________________ Date:__________________________________

Title of the project: ____________________________________________________________________

Website where you found the data:_______________________________________________________

Project Grade: __________________________________

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 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]

Lab Section Lab Partners) Gauss's Law Investigation #2: Charge Distributions on Conductors Introduction In Investigation #1, you discovered that the flux thru a closed surface (i.c., a Gaussian surface) is proportional to the charged enclosed by that surface: Flux thru Gaussian Surface & Charge enclosed by surface This relationship is known as Gauss's Law. In this investigation, you will use Gauss's Law to determine where charge is located on conducting objects of various shapes. Question 1 What is the electric field inside of the conducting material of any conductor? Question 2 Based on your answer to question 1, how many electric field lines are located inside of the conducting material of any conductor? The diagram at right shows a solid metal ball that bears an excess positive charge. When you studied electrostatics, you may have used reasoning about how charges attract and repel one another to determine where these charges lie on the metal ball. For now, however, it is important that you put this knowledge aside. The ultimate goal of this investigation is to help you learn how to apply Gauss's Law. Determining the locations of the excess charges on a conductor is just a bonus. Inside of the ball is a closed dotted path that represents a Gaussian surface. Remember that a Gaussian surface is a mathematical construct, not a real, physical object. Notice that the Gaussian surface is contained completely within the metallic material of the metal ball. Recall that the electric flux thru a closed surface is related to the number of field lines that pass thru that surface. Flux is positive if the field lines pass from inside to outside and is negative if the field lines pass from outside to inside. Question 3 What is the value of the electric flux thru the Gaussian surface shown in the diagram? Explain your reasoning.2) Given a uniform E-field, E = (2.001 - 3.00j + 4.00k) , and the Gaussian surface shown (a Rectangular Cuboid). There is no charge inside the surface. 1.50 m Calculate the Electric flux through each of the 6 surfaces: left, Pright, Ptop, 2.00 m 2.00 m Pbottom, Pfront, and @back. (show all your work, write down all the area vectors) X 1 BONUS POINT: What is the net flux through the Gaussian Surface if a Uranium nucleus is placed inside the Gaussian Surface? (HINT:use Gauss' Law) ZQuestion 2 |3 Mark|: Consider the following system of linear equations: 3.333(1t. + 15920x3 + [0.333; = T953. 2.222(1r. + 16.1104} + 9.6[203'3 = 0.965. -l.561|.t. + 5.l792.r2 - [.6355x3 = 2.7M. with actual solution: [1, 0.5, -1]. it. Use Gaussian elimination and three-digit rounding arithmetic to solve the above linear gm compare the approximations to the actual solution. b. Repeat the exercise using Gaussian elimination with partial pivoting. c. Repeat the exercise using Gaussian elimination with sealed pivoting