How do I determine whether a point is significantly different from a predicted value based on a linear regression?

When you do linear regression, check the option to produce a table of residuals. Residuals are the distances of each point from the best fit line. Then analyze that column of residuals using Grubbs' test to test whether the largest value is a significant outlier. Grubbs' test is quite specific -- it asks if the largest deviation is a significant outlier. It isn't fair to ask about two or more outliers by recycling Grubbs' test. But other outlier tests have been developed.