Linear Regression Exercises

Simple Regression

Research Question: Does the number of hours worked per week (workweek) predict family income (income)?

Using Polit2SetA data set, run a simple regression using Family Income (income) as the outcome variable (Y) and Number of Hours Worked per Week (workweek) as the independent variable (X). When conducting any regression analysis, the dependent (outcome) variables is always (Y) and is placed on the y-axis, and the independent (predictor) variable is always (X) and is placed on the x-axis.

Follow these steps when using SPSS:

1. Open Polit2SetA data set.

2. Click on Analyze, then click on Regression, then Linear.

3. Move the dependent variable (income) in the box labeled “Dependent” by clicking the arrow button. The dependent variable is a continuous variable.

4. Move the independent variable (workweek) into the box labeled “Independent.”

5. Click on the Statistics button (right side of box) and click on Descriptives, Estimates, Confidence Interval (should be 95%), and Model Fit, then click on Continue.

6. Click on OK.

Assignment: Through analysis of the SPSS output, answer the following questions. Answer questions 1 – 10 individually, not in paragraph form

1. What is the total sample size?

2. What is the mean income and mean number of hours worked?

3. What is the correlation coefficient between the outcome and predictor variables? Is it significant? How would you describe the strength and direction of the relationship?

4. What it the value of R squared (coefficient of determination)? Interpret the value.

5. Interpret the standard error of the estimate? What information does this value provide to the researcher?

6. The model fit is determined by the ANOVA table results (F statistic = 37.226, 1,376 degrees of freedom, and the p value is .001). Based on these results, does the model fit the data? Briefly explain. (Hint: A significant finding indicates good model fit.)

7. Based on the coefficients, what is the value of the y-intercept (point at which the line of best fit crosses the y-axis)?

8. Based on the output, write out the regression equation for predicting family income.

9. Using the regression equation, what is the predicted monthly family income for women working 35 hours per week?

10. Using the regression equation, what is the predicted monthly family income for women working 20 hours per week?

For this assignment, answer question 1 through 10 individually. DO NOT ANSWER IN PARAGRAPH FORM.

Multiple Regression

Assignment: In this assignment we are trying to predict CES-D score (depression) in women. The research question is: How well do age, educational attainment, employment, abuse, and poor health predict depression?

Using Polit2SetC data set, run a multiple regression using CES-D Score (cesd) as the outcome variable (Y) and respondent’s age (age), educational attainment (educatn), currently employed (worknow), number, types of abuse (nabuse), and poor health (poorhlth) as the independent variables (X). When conducting any regression analysis, the dependent (outcome) variables is always (Y) and is placed on the y-axis, and the independent (predictor) variable is always (X) and is placed on the x-axis.

Follow these steps when using SPSS:

1. Open Polit2SetC data set.

2. Click on Analyze, then click on Regression, then Linear.

3. Move the dependent variable, CES-D Score (cesd) into the box labeled “Dependent” by clicking on the arrow button. The dependent variable is a continuous variable.

4. Move the independent variables (age, educatn, worknow, and poorhlth) into the box labeled “Independent.” This is the first block of variables to be entered into the analysis (block 1 of 1). Click on the bottom (top right of independent box), marked “Next”; this will give you another box to enter the next block of indepdent variables (block 2 of 2). Here you are to enter (nabuse). Note: Be sure the Method box states “Enter”.

5. Click on the Statistics button (right side of box) and click on Descriptives, Estimates, Confidence Interval (should be 95%), R square change, and Model Fit, and then click on Continue.

6. Click on OK.

Assignment: (When answering all questions, use the data on the coefficients panel from Model 2). Answer questions 1 – 5 individually, not in paragraph form

1. Analyze the data from the SPSS output and write a paragraph summarizing the findings. (Use the example in the SPSS output file as a guide for your write-up.)

2. Which of the predictors were significant predictors in the model?

3. Which of the predictors was the most relevant predictor in the model?

4. Interpret the unstandardized coefficents for educational attainment and poor health.

5. If you wanted to predict a woman’s current CES-D score based on the analysis, what would the unstandardized regression equation be? Include unstandardized coefficients in the equation.

For this assignment, answer question 1 through 5 individually. DO NOT ANSWER IN PARAGRAPH FORM.

Required Readings

Gray, J.R., Grove, S.K., & Sutherland, S. (2017). Burns and Grove’s the practice of nursing research: Appraisal, synthesis, and generation of evidence (8th ed.). St. Louis, MO: Saunders Elsevier.

Chapter 24, “Using Statistics to Predict”

This chapter asserts that predictive analyses are based on probability theory instead of decision theory. It also analyzes how variation plays a critical role in simple linear regression and multiple regression.

Statistics and Data Analysis for Nursing Research

Chapter 9, “Correlation and Simple Regression” (pp. 208–222)

This section of Chapter 9 discusses the simple regression equation and outlines major components of regression, including errors of prediction, residuals, OLS regression, and ordinary least-square regression.

Chapter 10, “Multiple Regression”

Chapter 10 focuses on multiple regression as a statistical procedure and explains multivariate statistics and their relationship to multiple regression concepts, equations, and tests.

Chapter 12, “Logistic Regression”

This chapter provides an overview of logistic regression, which is a form of statistical analysis frequently used in nursing research.

Optional Resources

Walden University. (n.d.). Linear regression. Retrieved August 1, 2011, from http://streaming.waldenu.edu/hdp/researchtutorials/educ8106_player/educ8106_linear_regression.html

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Discussion Questions (DQ)

Initial responses to the DQ should address all components of the questions asked, including a minimum of one scholarly source, and be at least 250 words. Successful responses are substantive (i.e., add something new to the discussion, engage others in the discussion, well-developed idea) and include at least one scholarly source. One or two-sentence responses, simple statements of agreement or “good post,” and responses that are off-topic will not count as substantive. Substantive responses should be at least 150 words. I encourage you to incorporate the readings from the week (as applicable) into your responses.

Weekly Participation

Your initial responses to the mandatory DQ do not count toward participation and are graded separately. In addition to the DQ responses, you must post at least one reply to peers (or me) on three separate days, for a total of three replies. Participation posts do not require a scholarly source/citation (unless you cite someone else’s work). Part of your weekly participation includes viewing the weekly announcement and attesting to watching it in the comments. These announcements are made to ensure you understand everything that is due during the week.

APA Format and Writing Quality

Familiarize yourself with the APA format and practice using it correctly. It is used for most writing assignments for your degree. Visit the Writing Center in the Student Success Center, under the Resources tab in Loud-cloud for APA paper templates, citation examples, tips, etc. Points will be deducted for poor use of APA format or absence of APA format (if required). Cite all sources of information! When in doubt, cite the source. Paraphrasing also requires a citation. I highly recommend using the APA Publication Manual, 6th edition.

Use of Direct Quotes

I discourage over-utilization of direct quotes in DQs and assignments at the Master’s level and deduct points accordingly. As Masters’ level students, it is important that you be able to critically analyze and interpret information from journal articles and other resources. Simply restating someone else’s words does not demonstrate an understanding of the content or critical analysis of the content. It is best to paraphrase content and cite your source.

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Late Policy

The university’s policy on late assignments is a 10% penalty PER DAY LATE. This also applies to late DQ replies. Please communicate with me if you anticipate having to submit an assignment late. I am happy to be flexible, with advance notice. We may be able to work out an extension based on extenuating circumstances. If you do not communicate with me before submitting an assignment late, the GCU late policy will be in effect. I do not accept assignments that are two or more weeks late unless we have worked out an extension. As per policy, no assignments are accepted after the last day of class. Any assignment submitted after midnight on the last day of class will not be accepted for grading.

Communication

Communication is so very important. There are multiple ways to communicate with me: Questions to Instructor Forum: This is a great place to ask course content or assignment questions. If you have a question, there is a good chance one of your peers does as well. This is a public forum for the class. Individual Forum: This is a private forum to ask me questions or send me messages. This will be checked at least once every 24 hours.

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Linear Regression Exercises