Final answer:
The residuals in a scatter plot represent the difference between the observed and predicted values. The slope and y-intercept of the regression line tell us about the relationship between the variables. The fit of the regression line can be assessed by examining the residuals for patterns.
Step-by-step explanation:
The residuals in a scatter plot represent the difference between the observed values and the predicted values. They measure how far off the regression line the actual data points are. Residuals can be positive if the observed value is higher than the predicted value, or negative if it is lower.
The slope of the regression line represents the rate of change between the independent variable (x) and the dependent variable (y). It tells us how the y variable changes for every unit increase in x. The y-intercept represents the value of y when x is 0, or the starting point of the regression line.
To determine how well the regression line fits the data, we can look at the residual plot. If the residuals are randomly scattered around zero and show no clear pattern, it suggests that the regression line is a good fit for the data. If there is a pattern or the residuals are consistently positive or negative, it indicates that the regression line does not fit the data well.