Final answer:
A residual is the difference between an actual data point's response value and the predicted value from a regression analysis. The slope and y-intercept of the regression line describe the rate of change and the expected value when the independent variable equals zero, respectively. Outliers can significantly affect the fit of the regression model.
Step-by-step explanation:
The difference between the response value of an actual data point and the predicted value by regression is called a residual. In the context of regression analysis, a residual is the error term representing the amount by which the prediction of the dependent variable, based on the linear regression model, differs from the actual observed value. The least-squares regression line is calculated in such a way as to minimize the sum of the squared residuals, known as the sum of squared errors (SSE). the slope of the regression line tells us the rate at which the dependent variable changes for a unit change in the independent variable. The y-intercept is the value of the dependent variable when the independent variable is zero. These both provide critical information about the relationship between the two variables being studied.
Outliers can greatly affect the regression model. They are typically identified as points lying more than two standard deviations of the residuals from the regression line. When considering outlier identification, both the distance from the regression line (residual size) and the leverage (potential to impact the regression line's slope and intercept) are taken into account.