Correlations and Regression

Faculty of Arts Part IV: Correlations and Regression

PSYC 2101 Statistics in the Social Sciences

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Table of Contents

Part IV. Correlations and Regression Weeks 9, 10, & 11 (suggested)

• Chapter 14: Correlation and Regression

• Learning Objectives

• Study Plan

• Practice Exercises for Chapter 14

• SPSS (Optional Activity)

• Review of Learning Objectives

• Summary of Part IV. Correlations and Regression

• Assignment 4: Correlations and Regression

Part IV: Correlations and Regression (Weeks 9, 10, & 11)

• Correlation and regression provide tools for understanding relationships between variables and predicting values.

• Correlation examines strength and direction of relationships between two variables.

• Regression analysis assesses how one or more independent variables can predict another variable (dependent variable).

• Key concept: Importance of determining the degree and direction of relationships, as well as predicting values based on variable relationships.

Chapter 14: Correlation and Regression

Learning Objectives

• After completing Chapter 14, students should be able to:

  • Describe and draw three types of scatter plots: positive, negative, and zero.

  • Compare and contrast four correlation types: Pearson, Spearman, Point-biserial, and Phi correlations.

  • Compute Pearson, Spearman, Point-biserial, and Phi correlations.

  • Test significance of correlations using either the t-test or critical value tables.

  • Explain the concept of a linear equation, slope, and Y-intercept.

  • Define least-squared-error solution.

  • Compute the linear regression equation to predict Y values from X values.

  • Test the significance of the regression equation using the F-ratio.

Study Plan

1. Read Chapter 14: Correlation and Regression (pages 478-523).

2. Complete practice exercises and check solutions at the end of the Study Guide.

3. Solve odd-numbered problems (pages 528-531).

Practice Exercises for Chapter 14

Practice Exercise 1

• Investigate the relationship between average hours of sleep for athletes before competition and number of medals won.

  1. Calculate the Pearson correlation.

  2. Determine significance at α = 0.05 (two-tailed) using Table B.6, "Critical Values for the Pearson Correlation".

  3. Conduct a five-step hypothesis test using the two-tailed t-test (α = 0.05).

  • Data:

  • Average Hours of Sleep: [8, 8, 7, 7, 6, 6]

  • No. of Medals: [5, 4, 5, 3, 3, 2]

Practice Exercise 2

• Compare Pearson correlation coefficient with Spearman correlation obtained from Exercise 1.

  1. Rank both datasets and compute Spearman correlation using formulas from textbook pages 501-502.

  2. Compare results and discuss conclusions.

Practice Exercise 3

• Explore the relationship between pet ownership and self-esteem.

  • Data:

  • Self-esteem scores and pet ownership status (1=own pet, 0=do not own pet).

  1. Compute point-biserial correlation.

  2. Calculate the coefficient of determination and draw conclusions about the relationship.

Practice Exercise 4

• Investigate the relationship between having a college degree and being promoted after the first year of employment.

  • Data:

  • Utilize binary scoring (1=degree & promoted, 0=degree not & not promoted).

  1. Calculate phi correlation.

  2. Assess strength via the coefficient of determination (r²) and interpret findings.

Practice Exercise 5

• Predict GPA based on hours of independent study per course.

  • Data:

  • Hours of Study and corresponding GPAs.

  1. Determine values of linear regression equation (a, b).

  2. Assess significance of the regression equation via F-ratio (α = 0.01).

SPSS (Optional Activity)

• Detailed instructions for computing correlation and regression through SPSS are provided on pages 524–528.

• Familiarizing oneself with this procedure is advantageous for conducting research involving variable relationships and regression analyses.

Review of Learning Objectives

• Revisit Learning Objectives for Chapter 14 to assess achievement.

• Self-evaluation is encouraged to document feedback on objective mastery.

• For any uncertainties regarding objectives, review material and contact Open Learning Faculty Member.

• Reminder: Register for the final examination at least one month prior to the examination date.

Summary of Part IV: Correlations and Regression

• Key learnings include constructing scatter plots and determining correlation types through observed patterns.

• Rationale behind correlations and computation methods for Pearson, Spearman, Point-biserial, and Phi correlations were discussed.

• Tested significance of correlations, and understanding of regression towards the mean.

• Introduced concepts of linear equations, regression, least-squared error solutions, and significance testing of regression equations.

Assignment 4: Correlations and Regression

• Completion of Assignement 4: Correlations and Regression is required, contributing 8% towards final course grade.

• Instructions for submitting the assignment are available in the Assignments Overview area of the course.

• Adhere to recommended title page format for submission.