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What is Regression?

In a sense, a well-fitting line drawn through the plot of a strong correlation gives us a tool for predicting the performance of a variable on one measure if we know it's score on the other. Informally, most humans do regression, which is the process of predicting future outcomes based on past performance. Let's say your scores on the past 3 tests in a class have been 75, 82 and 85. What prediction would you likely make about your performance on the last test? Explain your conclusion.

In order to do this formally, in the statistical arena, we need to make an effort to assess the dependability or reliability of the past as a guide to the future. We will use some of the tools we've acquired to this point, and learn a few new ones. Sometimes when we try to do this prediction, we use the mean. Let's say that we are planning a trip to Rome, Italy in September. We need to pick a suitable wardrobe. We do some research and discover that the mean daytime temperature in Rome at that time of year is 75., so that is our best prediction. The mean nighttime temperature is 45 so now we will be appropriately prepared for our time outdoors, day or night.

In many situations we have a lot more information than this to work from. We may have an entire distribution of observations, so we can figure the mean and standard deviation. If we are looking at our own score in relation to the others, we can interpret the meaning of its difference from the mean by doing a transformation and using z-scores.

However, as much as we can speculate on future performance based on the above-mentioned statistics, they really aren't sufficient for predictions that we can have some confidence about. We need to use our recently gained correlation skills to help us understand the relationship between the two variables.