Regression analysis consist of four steps. In the previous video, I explained the first two steps. This video, I will explain you how to perform a residual check to validate the results. In the next video, I will show you what a prediction interval is. Remember that we were studying is the number of production stops was an influence factor for the number of broken defect teabags. These are the results we found. The formula represents the best fitting line. The P value indicates that the results are statistically significant. And the R squared is really high and indicates that the number of production stops explains the behavior of our defect bags for very large part. These were the first two step of regression analysis. Before we can completely trust our conclusions however, we have to verify the underlying assumptions of regression analysis. And this is called the residual analysis. We have to check if the residuals are normally distributed and if the residuals do not show any outliers or other irregularities. But what is a residual? Let's take a look at the fitted line plot. The dots represent the data and the line is the best fitted value based on the regression line for that number of stops. There is a difference though between the data and the fitted value, and this difference is called the residual. Residuals are calculated by subtracting the observed value, the data, from the fitted value, the estimated regression line. To perform a residual analysis, we can go to Minitab. So pause the video, load this data set into your Minitab, before you continue watching. Your loaded data into Minitab should look like this, with a column days, a column bags, and a column stops. Let's study the residuals. For that, we have to go back to the regression menu, which we've found under stat, regression, and the fitted line plots. Maybe you're still there but otherwise, fill in your response again which was bags. And fill in your influence factor which was stops. Okay, now, the residual analysis can be found under graphs. And here we have residual plots. If you ask for the four in one, we get them all in one go. Okay, and okay again. Now, this is your residual plots for your analysis of the defect bags. Let's take a look at the four in one plot. Remember that we needed to check two things in the residual analysis. Let's start with the normality assumptions. Are the residuals normally distributed? It looks likes they are. Now, move onto the second step. Do you see any outliers or irregulatory? It doesnâ€™t look like there are any. It means that we can trust the conclusions from our regression and analysis as the assumptions are satisfied. However, what if we would have had different residuals like these ones? This normal probability plot shows that the residuals are not normally distributed, because they are in a curved line instead of a straight one. This graph also shows a few outliers. In such case, the conclusion from the regression analysis should be treated with caution. And depending on what the violation of the assumptions are, you can try different things to solve this. If you have outliers, a possible way is to delete them and see if the results of your regression change a lot. Compare your model under both situations. If it is a non-linearity problem, try a quadratic regression model. Which is discussed in the next video. Regression analysis can be easily extended to deal with many different situations. But, that is a topic that is outside of the scope of this video series. In summary, you will learn to perform a residual check for your regression analysis. If the residuals are normally distributed and show no outliers or irregularities, this means that your assumptions are met. If the assumptions are not met, you have to be careful to interpret your results.