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 Note that the slope of the regression equation for standardized variables is r. Where Z Y' is the predicted standard score for Y, r is the correlation, and Z X is the standardized score for X. 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. Regression is a statistical approach that suggests predicting a dependent variable (goal feature) with the help of other independent variables (data). The least squares regression equation is listed at the top along with the observed correlation. Note that the calculations have all been shown Click Compute to view the regression results as shown below. The slope (b) can be calculated as follows:Īnd the intercept (A) can be calculated as Simple Linear Regression An analysis appropriate for a quantitative outcome and a single quantitative ex-planatory variable. 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 simplest form of the regression equation with one dependent and one independent variable is defined by the formula y c + bx, where y estimated. 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 A simple linear regression (also known as a bivariate regression) is a linear equation describing the relationship between an explanatory variable and an. You may have noticed that we did not specify what
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