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Module 7: Correlation and Regression Assignment

Questions are taken directly from Brase, Brase, Dolor, and Seibert Chapter 9, pages 541. In case an eBook page number differs, the questions are listed below:

The most important questions in life usually cannot be answered with absolute certainty. Many important questions are answered by giving an estimate and a measure of confidence in the estimate. This was the focus of Chapter 7. However, sometimes important questions must be answered in a more straightforward manner by a simple yes or no. Hypothesis testing is the statistical process of answering questions with a straightforward yes or no and providing an estimate of the risk in accepting the answer.

1. What do we mean when we say that two variables have a strong positive (or negative) linear correlation? What would a scatter diagram for these variables look like? Is it possible that two variables could be strongly related somehow but have a low linear correlation? Explain and draw a scatter diagram to demonstrate your point.

2. What do we mean by the least-squares criterion? Give a very general description of how the least-squares criterion is involved in the construction of the least-squares line. Why do we say the least-squares line is the “best-fitting” line for the data set?

3. In this chapter [9], we discussed three measures for the “goodness of fit” of the least-squares line for given data. These measures were standard error of estimate, correlation coefficient, and coefficient of determination. Discuss the ways in which these measurements are different and the ways in which they are similar to each other. Be sure to include a discussion of explained variation, unexplained variation, and total variation in your answer. Draw a sketch and include appropriate formulas.

4. Look at the formula for confidence bounds for least-squares predictions. Which of the following conditions do you think will result in a shorter confidence interval for a prediction?

a. Larger or smaller values for the standard error of estimate

b. Larger or smaller number of data pairs

c. A value of x near x¯ or a value of x far away from 𝑥𝑥¯

5. Why would a shorter confidence interval for a prediction be more desirable than a longer interval?

CJUS 745

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For many applications in statistics, more data leads to more accurate results. In multiple regression, we have more variables (and data) than we have in most simple regression problems. Why will this usually lead to more accurate predictions? Will additional variables always lead to more accurate predictions? Explain your answer. Discuss the coefficient of multiple determination and its meaning in the context of multiple regression. How do we know if an explanatory variable has a statistically significant influence on the response variable? What do we mean by a regression model?

6. Use the Internet or go to the library and find a magazine or journal article in your field of major interest to which the content of this chapter could be applied. List the variables used, method of data collection, and general type of information and conclusions drawn.

General Instructions

As doctoral students, your assignments are expected to follow the principles of high-quality scientific standards and promote knowledge and understanding in the field of criminal justice. You should apply a rigorous and critical assessment of a body of theory and empirical research, articulating what is known about the phenomenon and ways to advance research about the topic under review. Research syntheses should identify significant variables, a systematic and reproducible search strategy, and a clear framework for studies included in the larger analysis.

Assignments may be written in first person (“I”).

All assignments should be clearly and concisely written, with technical material set off. Please do not use jargon, slang, idioms, colloquialisms, or bureaucratese. Use acronyms sparingly and spell them out the first time you use them. Please do not construct acronyms from phrases you repeat frequently in the text.

Structure of Assignment Paper

For purposes of this assignment, there is no layout structure required as far as the setup of this paper, with one exception. I would appreciate it if you used separate headers for question 1 and question 2. Sub-headers are also allowed but not required. Questions should strive to be no less than 250 words each with no maximum limit.

I expect all papers to be in the latest APA edition, properly cited, and all tables attached.

Note: Your assignment will be checked for originality via the Turnitin plagiarism tool.