Math 227 Project 1: Exploring Relationships Between two Variables

In this project, you will search two quantitative variables that may have a linear correlation. describe and analyze the relationship between the variables the way it is explained in Chapter 4 (4.1-4.2). hen, 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.Possible websites to look for 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.

http://maps.latimes.com/neighborhoods/income/median/neighborhood/list/ for Median Household Income Ranking in Los Angeles

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 on the last page for the full table) 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.

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 differ (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

summarize the findings