Suppose it's known that a new labor saving device is in place, increasing accuracy and allowing more time for sleep. Alternatively, a physical malady might keep a worker up at night as well as reduce his concentration during the day. Gathering more data or expanding the regression model to include the presence of disease and the use of labor saving devices are two suggestions for improving the study of sleep and production quality. The error term in a simple linear regression model is assumed to follow a normal distribution, be independent of each other and have constant variability for all points in the sample. Figure 3 summarizes the formal assumptions.
Problems arise when certain assumptions fail to be met.
An analyst's success in building a good predictive regression model depends on conducting various tests that help to determine if assumptions likely prevail. Interpreting the alpha is fraught with problems so the beta estimate typically takes center ring. Its sign and magnitude both indicate the nature of the association in the past. Assuming that history repeats itself, the beta estimate can be used to predict the future relationship. Figure 4 summarizes a regression model focused on the relationship between U.S. dollar interest rate swap and Treasury Notes.