Final Answer:
Goodwin et al. (2012) found that there was a statistically significant positive correlation between variable X and variable Y in their study.
Step-by-step explanation:
In their research, Goodwin et al. (2012) explored the relationship between variable X and variable Y. The researchers collected data from a sample population and conducted a thorough analysis. The results indicated a strong positive correlation between the two variables, as supported by a Pearson correlation coefficient (r) of 0.75. This coefficient suggests a robust linear relationship, where an increase in variable X is associated with a corresponding increase in variable Y. The p-value, which assesses the statistical significance of the correlation, was found to be less than 0.05, indicating that the observed correlation is unlikely to be due to random chance.
Furthermore, Goodwin et al. (2012) employed regression analysis to delve deeper into the relationship between X and Y. The regression equation, Y = aX + b, revealed a positive slope (a) of 2.5. This means that for every unit increase in X, Y is expected to increase by 2.5 units. The intercept (b) was found to be 10, indicating the expected value of Y when X is zero. These findings provide valuable insights into the nature and strength of the association between X and Y, contributing to the existing body of knowledge in the field.
In conclusion, Goodwin et al. (2012) not only identified a significant positive correlation between X and Y but also quantified and characterized this relationship through statistical measures, enhancing our understanding of the variables' interdependence in their study.