That there is a strong positive relationship. We now consider how we could predictĪ student's university GPA if we knew his or her high school GPA.įigure 3 shows a scatter plot of University GPAĪs a function of High School GPA. High school and university grades for 105 computer science majorsĪt a local state school. The case study " SAT and College GPA" contains A response variable can be predicted based on a very simple equation: Regression equation: +. Note that the slope of the regression equation for standardized variables is r. This calculator will determine the values of b and a for a set of data comprising two variables, and estimate the value of Y for any specified value of X. Where Z Y' is the predicted standard score for Y, r is the correlation, and Z X is the standardized score for X. The line of best fit is described by the equation bX + a, where b is the slope of the line and a is the intercept (i.e., the value of Y when X 0). The regression equation is simpler if variables are standardized so that their means are equal to 0 and standard deviations are equal to 1, for then b = r and A = 0. The formulas are the same simply use the parameter valuesįor means, standard deviations, and the correlation. In terms of sample statistics rather than population parameters. Note that the calculations have all been shown The slope (b) can be calculated as follows:Īnd the intercept (A) can be calculated as Statistics for computing the regression line. Standard deviation of Y, and r is the correlation between M X is the mean of X, M Y is the mean of Y, s X is The calculations are based on the statistics shown However, theĬalculations are relatively easy, and are given here for anyone who Is typically computed with statistical software. In the age of computers, the regression line Where Y' is the predicted score, b is the slope The sum of the squaredĮrrors of prediction shown in Table 2 is lower than it would be "best-fitting line." By far, the most commonly-used criterionįor the best-fitting line is the line that minimizes the sum of You may have noticed that we did not specify what
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