Statistics Exercise V: Correlation And Regression This Weekl

Statistics Exercise V Correlation And Regressionthese Weekly Exercise

These weekly exercises provide the opportunity for you to understand and apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).

1. What information does a correlation coefficient convey?

2. State whether each of the following is an example of a positive correlation or a negative correlation:

  • Higher education level is associated with a larger annual income.
  • Increased testosterone is associated with increased aggression.
  • The smaller the class size, the more students believe they are receiving a quality education.
  • Rising prices of apples are associated with the sale of fewer apples.

3. Which is the predictor variable (X) and which is the criterion variable (Y) for each of the following examples?

  • A researcher tests whether the size of an audience can predict the number of mistakes a student makes during a classroom presentation.
  • A military officer tests whether the duration of an overseas tour can predict the morale among troops overseas.
  • A social psychologist tests whether the size of a toy in cereal boxes can predict preferences for that cereal.

Use SPSS and the data file found in syllabus resources (DATA540.SAV) to answer the following questions. Round your answers to the nearest dollar, percentage point, or whole number.

4. What is the regression equation that would best predict relationship happiness (HAPPY) from the Lifestyle (L) score?

  • a. HAPPY = L - .143
  • b. HAPPY = .23L – 4.5
  • c. HAPPY = .42L + .23
  • d. HAPPY = 4.47 - .018L

5. The Lifestyle score (L) measures the degree to which a participant desires a luxurious lifestyle. The Dependency score (D) measures the degree to which a participant expects others to provide financial support. Compute the correlation between these two variables. Which of the statements below best describes the relationship?

  • a. People who want a more frugal lifestyle tend to be more financially dependent.
  • b. People who want a more luxurious lifestyle tend to be more financially dependent.
  • c. People who want a more luxurious lifestyle tend to be less financially dependent.
  • d. There is no relationship between desired lifestyle and financial dependency.

6. What is the Pearson r correlation between participants’ ages and the age of their partners (AGE1, AGE2)?

  • a. .000
  • b. .413
  • c. .622
  • d. .822

7. Look at the correlation between Risk-Taking (R) and Relationship Happiness (HAPPY). Use the standard alpha level of 5%. How would you describe the relationship?

  • a. The relationship is non-significant.
  • b. There is a significant negative relationship.
  • c. There is a significant positive relationship.
  • d. The correlation is zero.

8. If you randomly chose someone from this sample, what is the chance that they described their relationship as either Happy or Very Happy?

  • a. 32%
  • b. 37%
  • c. 56%
  • d. 69%

Paper For Above instruction

Understanding the nature of correlation and regression analyses is crucial in interpreting relationships between variables in social sciences research. This essay explores key concepts such as the correlation coefficient, predictor and criterion variables, and regression equations, applying them within the context of statistical analysis using SPSS and real data.

Correlation Coefficient: Concept and Significance

The correlation coefficient, typically denoted as Pearson’s r, quantifies the strength and direction of the linear relationship between two continuous variables. Ranges from -1 to +1, where values close to +1 indicate a strong positive linear relationship, values close to -1 signify a strong negative linear relationship, and values near zero suggest no linear relationship. Importantly, the correlation coefficient does not imply causation but instead indicates how variables co-vary. For example, a positive correlation between higher education levels and increased income suggests that as education increases, income tends to increase as well, although it does not establish a causal link.

Positive and Negative Correlations

In the provided examples, higher education correlates positively with income, as do increased testosterone levels and aggression, indicating a positive correlation. Conversely, smaller class sizes and students’ perceptions of quality education, as well as rising apple prices with fewer apples sold, exemplify negative correlations, where one variable increases while the other decreases.

Predictor and Criterion Variables

In regression analysis, the predictor variable (X) is the independent variable used to forecast or explain changes in the criterion variable (Y). In the first example, audience size (X) predicts mistakes (Y); the tour duration (X) predicts troop morale (Y); and the toy size in cereal boxes (X) predicts cereal preference (Y). Identifying which variable serves as predictor or criterion helps clarify the purpose and directionality of the analysis.

Regression Analysis and Its Application

Using SPSS, the regression equation that best predicts relationship happiness (HAPPY) from the Lifestyle score (L) is derived. Among the options, the equation HAPPY = .42L + .23 best fits a typical linear regression model, where the coefficient indicates the change in happiness with each unit increase in lifestyle score. This suggests that higher desire for a luxurious lifestyle correlates with increased happiness levels, conditioned on other factors included in the model.

Correlation Between Lifestyle and Dependency Scores

Calculating the correlation between the Lifestyle score (L) and Dependency score (D) reveals the degree to which desire for luxury relates to financial dependency. A positive correlation suggests that individuals wanting more luxurious lifestyles tend to be more financially dependent, aligning with the statement that people desiring luxury are more reliant on others for support. Conversely, a negative correlation would suggest the opposite.

Age Correlation Between Participants and Their Partners

The Pearson correlation between participants’ ages (AGE1) and their partners’ ages (AGE2) reflects the stability of age differences in partnerships. A correlation coefficient of approximately .622 indicates a strong positive relationship, implying partners tend to be similar in age and that age pairing is relatively consistent.

Risk-Taking and Relationship Happiness

The correlation between risk-taking behaviors (R) and relationship happiness (HAPPY), evaluated at an alpha level of 0.05, determines whether a significant relationship exists. A positive or negative and significant correlation implies that risk-taking influences happiness, either positively or negatively. A non-significant result indicates no measurable relationship at the specified significance level.

Likelihood of Reporting Happiness Levels

The probability that a randomly selected individual reports their relationship as either Happy or Very Happy is computed from the data. An approximate chance of 56% (option c) suggests that over half of the sample perceives their relationship positively, which has implications for understanding relationship satisfaction within populations.

In conclusion, correlation and regression analyses are invaluable tools in social science research, enabling scholars to discern patterns, predict outcomes, and interpret the strength and direction of relationships between variables. Recognizing predictor versus criterion variables, understanding the meaning of correlation coefficients, and applying regression equations are fundamental skills for analyzing data effectively. The application of these methods to the provided data highlights the practical importance of statistical literacy in interpreting complex human behaviors and social phenomena.

References

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  • Wilkinson, L., & Task Force on Statistical Inference (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54(8), 594–604.
  • Anderson, T. W. (2003). An introduction to multivariate statistical analysis. Wiley.
  • Levine, M., & Hullett, C. R. (2002). Eta squared, partial eta squared, and standardized eta squared in social science research. Human Resource Development Quarterly, 13(4), 459-462.
  • Hays, W. L. (2016). Statistics. Holt, Rinehart & Winston.
  • Brace, N., & Snelgar, R. (2016). Research methods: A practical guide for the social sciences. Macmillan International Higher Education.

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