We have created a regression model. Now, we are going to interpret the results, which tell us how successful our model is. But first, we need to get familiar with some basic statistics. In the broadest terms, the aim of each model is to represent real-life phenomena. All models differ in accuracy, or how well they depict reality. In statistics, we call the accuracy of the model its fit. The fit of a model is better if the difference between real data (that we measured) and predicted data (based on our model) is smaller.
We tried to predict cortisol level during maximum effort based on cortisol level during rest. Actual data points are represented with the circles, and the predictions that we made based on our model are vertically projected on the line (shown in the previous screenshot). As you can see, some circles lie almost on the line, some are above, and some are below the line. But the line is positioned so that these differences are minimized. If we want to estimate how good our model is, we should estimate the size of these differences. But, since the differences have both positive and negative values (some points are above and some are below the line), we can not just simply sum it up because they would cancel out. That's why we first need to square each difference and then sum it up. The result is sum squared error (SSE)—that is a measure of our model's error, or how much it deviates from actual data. In order to estimate the goodness of our model's fit, we need to compare the size of that deviation with a benchmark. The most commonly used benchmark is the simple average of y value or the flat, horizontal line. Comparison of our model and baseline gives us R-squared. The bigger the R-squared is, the smaller the probability that we obtained it by chance. The conventionally accepted threshold of the probability is 0.05 and is denoted by the p-value (significance) in our output. If our p-value is smaller than the threshold, we can conclude that we have enough evidence to believe that our model is good enough. In our case, the p-value is much smaller than the mentioned threshold, so we can assume that the cortisol level during the maximum effort can be reasonably well predicted based on the cortisol level at rest. We can conclude that we have created a successful model of the relationship between these two variables. In the next chapter, we are going to use it to create predictions.