Thxt Review Ev \"predicting\" what is known in a correlation of two variables, we can predict what is . This is accomplished h},r placing a line in such a way that it passes irough the main cluster of dots in the scatterplot. Positive and negative errors avoided by squaring the difference between the predicted value and the achial value. Thus, the prediction line is referred to as the line or the hue. The search for the least squares prediction line would he a frustrating trial and error process, except for the prediction of the least squares equation, . In this equation, Y\" represents the value, and X represents the value. The other values in the equation must he computed. When the computation is complete, the equation has the very desirable property of minimizing the total of all squared predic'dve errors for known values of Y in the original correlation analysis. Note the Key Terms secon that this essentially,r defuies the least squares prediction equation. Two limitations exist for the application of the least squares prediction equation. [line is that predictions ma},r not be reliable if extended beyond the maximum value of X in the original data. Second, since iere is no proof of causeeffect in correlation, the desired effect simpljg.T may not occur. Graphs may be constructed to depict the prediction equation. However, this should he done for purposes and not for prediction. It is more accurate to make the actual prediction from the . The least squared prediction equation is designed to reduce error in prediction, but it does not eiirninate it. Therefore, we must estimate the amount of error, understanding that the smaller the error, the more accurate our prediction. The estimated predictive error is expressed by the . This represents a rough measure of the average amount by which l-mown Y values deviate from their predicted it\" values. The value of r is extremelyr important in relation to predictive error. 1iatfhen r = 1, the predictive error will be . The most accurate predictions can be made when r values represent relationships, whether positive or negative. Prediction should not be attempted when r values are representing weal-r or nonexistent relationships