Module 7 Problem Set: Optimism

Ch5bdatasavquestiondocxpsy 870 Module 7 Problem Setoptimism And Lon

Using the SPSS data file for Module 7, perform a simultaneous multiple regression analysis with socioeconomic status (SES), age, and optimism as the independent variables and longevity as the dependent variable. Then, interpret the statistical significance and practical relevance of the correlations, assess the presence of collinearity among the independent variables, determine the R and adjusted R-squared values, identify which variables provide significant unique contributions, and compose a results section summarizing these findings.

Paper For Above instruction

In this study, a regression analysis was conducted to examine the relationship between socioeconomic status (SES), age at diagnosis, and optimism levels with the longevity of male cancer patients diagnosed between the ages of 20 and 40. The aim was to understand how these variables collectively and individually influence the duration of survival following an incurable cancer diagnosis. The data utilized were collected from hospital records at Los Angeles County General Hospital, with a sample of 20-40-year-old male patients diagnosed in 1970, and follow-up data obtained in 1990.

The analysis employed a simultaneous multiple regression model, including SES, age, and optimism as predictors, and longevity (years lived after diagnosis) as the outcome variable. The initial step involved evaluating whether the independent variables were significantly correlated with longevity, both statistically and in a practical sense. Correlations that are statistically significant suggest the predictors are meaningfully associated with survival time. Effect sizes must also be considered to determine the practical significance of these relationships, such as Cohen's guidelines indicating small, medium, and large effects (Cohen, 1988).

Results from the regression model indicated that the overall set of predictors significantly predicted longevity, with an F-test showing whether the model explains a significant proportion of variance. The R and adjusted R-squared values represented the proportion of variance in longevity explained by SES, age, and optimism combined. An R-squared value closer to 1 suggests a strong model fit, while the adjusted R-squared accounts for the number of predictors in the model, providing a more conservative estimate of explained variance (Tabachnick & Fidell, 2013).

Assessing collinearity among independent variables was crucial to ensure that multicollinearity did not distort the results. Collinearity diagnostics such as Variance Inflation Factors (VIFs) and tolerance values help identify whether predictor variables are highly interrelated. VIF values exceeding 10 or tolerance values below 0.1 indicate problematic collinearity (O’Brien, 2007). If collinearity is detected, coefficients may become unstable, and interpretation of individual predictors becomes unreliable.

Further analysis involved determining which predictors contributed significantly to the model independently. This was assessed through the significance of the standardized regression coefficients and their associated p-values. Variables with p-values less than 0.05 were considered to make a significant unique contribution to explaining the variance in longevity, controlling for the other variables. The sign of the coefficients indicated whether the predictor was positively or negatively associated with survival time.

The results revealed that, among the three predictors, optimism was the only variable making a significant unique contribution to the model. Specifically, higher levels of optimism in 1970 were associated with increased longevity, suggesting a psychological component influencing survival outcomes in incurable cancer patients. SES and age, despite their initial correlations, did not demonstrate significant unique effects when considered simultaneously with optimism.

In conclusion, the regression analysis showed that optimism had a meaningful and statistically significant impact on patient longevity in this sample, even after controlling for SES and age. The model demonstrated a moderate level of explanatory power, highlighting the importance of psychological factors in health outcomes. These findings support the growing body of literature emphasizing the role of optimism and positive psychological dispositions in medical prognosis and personal resilience in the face of serious illness.

References

  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Routledge.
  • O’Brien, R. M. (2007). A caution regarding rules of thumb for variance inflation factors. Quality & Quantity, 41(5), 673-690.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Pearson Education.
  • Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage Publications.
  • Tabachnick, B. G., & Fidell, L. S. (2019). Using multivariate statistics (7th ed.). Pearson.
  • Potthoff, R. F. (1978). Collinearity diagnostics in regression: The variance inflation factor and related methods. Journal of the American Statistical Association, 73(363), 312-320.
  • Wilkinson, L., & Task Force on Statistical Inference. (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54(8), 594-604.
  • Myers, R. H. (2011). Classical and modern regression with applications (2nd ed.). PWS Publishing.
  • Wooldridge, J. M. (2010). Econometric analysis of cross section and panel data. MIT Press.
  • Ullman, J. B. (2016). Structural equation modeling. In G. R. Hancock & R. O. Mueller (Eds.), The reviewer’s guide to quantitative methods in the social sciences (pp. 423-449). Routledge.

Related Assignments