Week 7 Linear Regression Exercises SPSS Output Simple

Week 7 Linear Regression Exercises Spss Outputsimple Linear Regressi

Analyze the SPSS output provided in the exercises, including descriptive statistics, correlation coefficients, regression models, and ANOVA tables, to answer specific questions about the relationship between variables such as family income, hours worked, depression scores, and predictors like age, education, employment, abuse, and health. Interpret the findings, coefficients, model fit, and statistical significance to understand the predictive relationships between these variables in the context of regression analysis.

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Linear regression analysis serves as a fundamental statistical method for understanding and predicting the relationship between an independent variable and a dependent variable. In the context of the provided SPSS output, the analysis aims to explore how specific predictors, such as hours worked per week or demographic and health-related variables, influence outcomes like family income and depression scores. Through examining descriptive statistics, correlation coefficients, regression models, and significance testing, researchers can glean insights into the strength and nature of these associations.

Firstly, consider the simple regression examining how hours worked per week predicts family income. The descriptive statistics show that the mean family income prior month is approximately $1,485.49 with a standard deviation of $950, and the average hours worked per week is 33.52 hours with a standard deviation of 12 hours in the current job. The correlation coefficient (Pearson r) between hours worked and family income is 0.300, with a significance of p = 0.000, indicating a statistically significant moderate positive relationship. This suggests that as hours worked increase, family income tends to increase as well.

The regression output provides a value of R = 0.300, and consequently, R squared (the coefficient of determination) equals 0.090. This indicates that approximately 9% of the variance in family income can be explained by the number of hours worked per week. While this shows a modest level of explanatory power, it signifies that other factors also influence family income beyond hours worked alone. The standard error of the estimate is approximately $907.88, representing the average distance that observed income values fall from the predicted income based on the model. A lower standard error would suggest a more precise prediction.

The ANOVA table reports an F value of 37.226 with degrees of freedom (1, 377) and a p-value of 0.001. As the p-value is less than 0.05, the regression model fits the data significantly better than a model with no predictors, confirming that hours worked per week is a meaningful predictor of family income. The regression coefficient for hours worked indicates that each additional hour worked per week is associated with an approximate increase of $23.083 in family income, holding other factors constant. The intercept (constant term) is estimated at approximately $711.155, meaning that if a woman worked zero hours, her predicted family income would be around $711.16.

Using the regression equation Y’ = 711.155 + 23.083 workweek, predictions for specific hours include: for 35 hours per week, income equals approximately $711.155 + (23.083 35) = $711.155 + $808.905 ≈ $1,520.06. For 20 hours, income equals about $711.155 + (23.083 * 20) = $711.155 + $461.66 ≈ $1,172.81. These estimates illustrate the practical application of the regression model in predicting family income based on work hours.

Transitioning to the multiple regression analysis predicting CES-D depression scores, the data examines how variables such as age, education level, employment status, abuse, and health influence depression. The model summary indicates an R = 0.412 and R squared = 0.170, meaning 17% of the variance in depression scores is explained by these predictors. The change in R squared when adding abuse into the model is 0.076, which is statistically significant, signifying that recent abuse experiences contribute uniquely to the prediction of depression levels beyond other variables.

Reviewing the coefficients from the model, significant predictors include the CES-D score at Wave 1 and the number of types of abuse, as their p-values are below 0.05. The unstandardized coefficients reveal that each additional type of abuse is associated with an increase of roughly 2.772 points in depression score, after controlling for other variables. The Beta coefficients show that the CES-D Wave 1 score is the strongest predictor (Beta ≈ 0.360), followed by abuse, indicating these variables have substantial unique contributions to current depression.

Notably, the interventions based on this analysis highlight that recent abuse is significantly associated with increased depression severity, emphasizing the importance of addressing abuse in mental health assessments. The model's overall significance (p = 0.000) confirms its adequacy in predicting depression scores within the sample. In practical terms, the regression equation for predicting depression (Y) can be written as: CES-D score = 10.911 + 0.430 CESD_Wave1 + 2.772 number of abuse types. This model enables clinicians and researchers to estimate depression severity based on prior depression levels and abuse experiences for targeted interventions.

Overall, regression analysis in these contexts provides valuable insights into the predictive relationships between variables relevant to socioeconomic and mental health outcomes. While the models explain a modest proportion of variance, they underscore the importance of specific predictors such as working hours, abuse, and depressive symptoms, guiding further research and intervention strategies. Understanding the statistical outputs and their implications enhances the ability to apply these findings in real-world contexts effectively.

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