Final answer:
Identify an outlier by plotting the data set as a scatter plot and then calculating the regression equations with and without the outlier. The outlier is a point that is significantly far from the best-fit line and influences the slope and y-intercept of the regression equation.
Step-by-step explanation:
To identify an outlier and create a regression equation for bivariate data, begin by plotting a scatter plot using the given data points. The outlier can visually be identified as the point which does not align well with the other data points on the scatter plot. Specifically, it can be numerically identified as any point that sits more than two standard deviations from the best-fit line, sometimes calculated from the residuals (differences between the observed and predicted values).
To calculate the regression equations, use a graphing calculator or statistical software to perform linear regression on the data set, both including and excluding the identified outliers. The equation will be in the form of y = mx + b, where m represents the slope and b the y-intercept of the line.
To see how an outlier affects the regression line, compare the slope and y-intercept of the equations with and without the outlier, as well as the correlation coefficient r, which measures the strength of the linear relationship.