![]() The maximum capacity is determined by the individual the person stops when unable to go any further. The individual is then systematically run to maximum physical capacity. At specified time intervals, the speed at which the treadmill moves and the grade of the treadmill both increase. To examine peak physical activity, tests have been designed where an individual runs on a treadmill. Since the process of expending energy requires oxygen, one way to evaluate this is to look at the rate at which they use oxygen at peak physical activity. To assess physical conditioning in normal individuals, it is useful to know how much energy they are capable of expending. Using residual plots to help identify other good predictors The only difference between the plots is the scale on the horizontal axis. Should we also add the predictor duration to the model? Let's investigate! Upon regressing blood pressure on weight and age, obtaining the residuals, and plotting the residuals against the predictor duration, we obtain the following "residuals versus duration" plot: Suppose we fit the model with blood pressure as the response and age and weight as the two predictors. But, you'll soon learn that it's a straightforward extension of simple linear regression. We haven't yet learned about multiple linear regression models - regression models with more than one predictor. It appears that adding the predictor weight to the model already containing age would help to explain some of the remaining variability in the response. If a plot of the "new response" against a predictor shows a non-random pattern, it indicates that the predictor explains some of the remaining variability in the new (adjusted) response. In essence, you can think of the residuals on the y-axis as a "new response," namely the individual's diastolic blood pressure adjusted for their age. In general, if there is some non-random pattern to the plot, it indicates that it would be worthwhile adding the predictor to the model. This "residuals versus weight" plot can be used to determine whether we should add the predictor weight to the model that already contains the predictor age. The regression of the response diastolic blood pressure (BP) on the predictor age: The researcher measured the age (in years), weight (in pounds), duration of hypertension (in years), and diastolic blood pressure (in mm Hg) on a sample of n = 20 hypertensive individuals ( Blood Pressure data). A researcher is interested in determining which of the following - age, weight, and duration of hypertension - are good predictors of the diastolic blood pressure of an individual with high blood pressure. predictor plot is used to determine whether or not another predictor should be added to the model. Let's take a look at an example in which the residuals vs. predictor plot offers no new information. predictor plot is just a mirror image of the residuals vs. In essence, for this example, the residuals vs. The alcohol consumption of the five men is about 40, and hence why the points now appear on the "right side" of the plot. The five red data points should help you out again. predictor plot for the data set's simple linear regression model with arm strength as the response and level of alcohol consumption as the predictor: And, no data points will stand out from the basic random pattern of the other residuals. fits plot." That is, a well-behaved plot will bounce randomly and form a roughly horizontal band around the residual = 0 line. predictor plot" is identical to that of a "residuals vs. predictor plot can help to determine whether the predictor should be added to the model (and hence a multiple regression model used instead). On the other hand, if the predictor on the x-axis is a new and different predictor, the residuals vs. predictor plot offers no new information to that which is already learned by the residuals vs. ![]() For a simple linear regression model, if the predictor on the x-axis is the same predictor that is used in the regression model, the residuals vs. predictor plot." It is a scatter plot of residuals on the y-axis and the predictor ( x) values on the x-axis. ![]()
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