Final answer:
The slope of a regression line represents the average change in the dependent variable for a one-unit increase in the independent variable. In predictions using FICO credit score, it indicates how the probability of default changes with varying credit scores. The y-intercept represents the value of the dependent variable when the independent variable is zero, however, it may not be practically relevant in all real-world scenarios.
Step-by-step explanation:
Interpretation of the Slope and y-Intercept
The slope of a regression line tells us how the dependent variable, typically denoted as y, responds to changes in the independent variable, x. In the context of predicting the probability of default using FICO credit score, the slope indicates the average change in the probability of default for each one-unit increase in the credit score. A negative slope implies that as the FICO score goes up, the probability of default decreases. Conversely, a positive slope would imply that higher FICO scores are associated with an increased probability of default, which is generally counterintuitive to what we know about credit scores.
The y-intercept represents the value of the dependent variable when the independent variable is zero. In the context of regression involving credit scores, the y-intercept would be interpreted as the estimated probability of default when the FICO score is zero, which is typically not a practical scenario. Thus, while the y-intercept can provide insight into the behavior of the model, it is often not meaningful as a standalone figure without considering the scope of realistic credit score ranges.
An ecologist might use the slope of a regression line to predict changes in an environmental factor, as seen with the sparrow hawks example, where the slope (-0.3031) indicates that with each percentage increase in returning birds, the percentage of new birds decreases by approximately 30 percent. This is an application of the slope concept in other fields such as ecology.