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15 regression

# 15 regression - What Practitionors Nood to Know by Mark...

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What Practitionors Nood to Know. .. by Mark Kritzman How can we predict uncertain outcomes? We could study the relations between the uncertain variable to be predicted and some known variable. Suppose, for example, that we had to predict the change in profits for the airline industry. We might exjject to find a relation between GNP growth in the current period and airline profits in the subsequent period, because economic growth usually foreshadows business travel as well as personal travel. We can quantify this relation through a technique known as regression analysis. Regression analysis can be traced to Sir Francis Galton (1822-1911), an English scientist and anthro- pologist who was interested in determining whether or not a son's height corresponded to his father's height. To answer this question, Galton measured a sample of fathers and computed their average height. He then measured their sons and computed their average height. He found that fathers of above- average height had sons whose heights tended to exceed the average, Galton termed this phenomenon "regression toward the mean." Simple Lineair Regression To measure the relation b)etween a single indepen- dent variable (GNP growth, in our earlier example) and a dependent variable (subsequent change in airline profits), we can begin by gathering some data on each variable—for example, actual GNP growth in each quarter of a given sample period and the change in the airline industiy's profit over each subsequent quarter. We can then plot the intersects of these observations. The result is a scatter diagram such as the one shown in Figure A. The horizontal axis represents a quarter's GNP growth and the vertical axis represents the percent- age change in profits for the airline industry in the subsequent quarter. The plotted points in the figure indicate the actual percentage change in airline profits associated with a given level of GNP growth. They suggest a positive relation; that is, as GNP increases so do airline profits. The straight line slop- ing upward from left to right measures this relation. This straight line is called the regression line. It has been fitted to the data in such a way that the sum of the squared differences of the observed airline profits from the values along the line is minimized. The values along the regression line corresponding to the vertical axis represent the predicted change in airline profits given the corresponding prior quarter's GNP . . . About Regressions growth along the horizontal axis. The difference between a value predicted by the regression line and the actual change in airline profits is the error, or the residual. Given a particular value for GNP growth, we can predict airline profits in the subsequent quarter by multiplying the GNP growth value by the slope of the regression line and adding to this value the intercept of the line with the vertical axis. The equation is: Here 'Y^ equals the predicted percentage change in airline profits, a

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15 regression - What Practitionors Nood to Know by Mark...

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