Luckily, you will never have to compute the coefficient of multiple determination by hand. Ŷ is the predicted value of the dependent variable, y is the dependent variable mean,Īnd y is the dependent variable raw score. Where SSR is the sum of squares due to regression, SSTO is the total sum of squares, The coefficient of multiple determination can be defined in terms of sums of squares: When the regression equation fits the data well, R 2 will be large (i.e., close to 1) Measures the proportion of variation in the dependent variable that can be predicted from the set of independent

The coefficient of multiple determination To answer this question, researchers look at the coefficient of multiple determination (R 2). We still need toĪsk: How well does our equation fit the data? The fact that our equation fits the data better than any other linear equation does not guarantee that it fits the data well. That means this equation fits the data from which it was createdīetter than any other linear equation. This is the only linear equation that satisfies a least-squares criterion. So the least-squares regression equation can be re-written as: Here, we see that the regression intercept (b 0) is 23.156, the regression coefficient for IQ (b 1) is 0.509, and the regression coefficientįor study hours (b 2) is 0.467. Excel does all the hard work behind the scenes, and displays the result in a regression coefficients table: Time-consuming, labor-intensive process by hand. In the previous lesson, we showed how to assign values to regression coefficients, using matrix algebra - a Only unknowns are the regression coefficients so to specify the equation, we need to assign values The regression coefficients areī 0, b 1, and b 2. Which are denoted by x 1 and x 2, respectively. The independent variables are IQ and study hours, In this equation, ŷ is the predicted test score. Since we have two independent variables, the equation takes the following form: The first task in our analysis is to define a linear, least-squares regression equation to predict test score,īased on IQ and study hours. Let's review the output produced by Excel and see how it addresses each task. Assess the contribution of each independent variable (i.e., IQ and study hours) to the prediction.Assess how well the regression equation predicts test score, the dependent variable.Develop a least-squares regression equation to predict test score, based on (1) IQ and (2) the number of hours.Excel provides everything we need to address the tasks we defined for this sample problem.

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