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Analysis of Covariance-Comparing the Slopes-ECO6416

Analysis of Covariance-Comparing the Slopes-ECO6416 -...

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Analysis of Covariance: Comparing the Slopes Consider the following two samples of before-and-after independent treatments. Values of Covariate X and a Dependent Variable Y Treatment -I Treatment-II X Y X Y 5 11 2 1 3 9 6 7 1 5 4 3 4 8 7 8 6 12 3 2 We wish to test the following test of hypothesis on the two means of the dependent variable Y1, and Y2: H 0 : The difference between the two means is about a given value M. H a : The difference between the two means is quite different than it is claimed. Since we are dealing with dependent variables, it's natural to investigate the linear regression coefficients of the two samples; namely, the slopes and the intercepts. Suppose we are interested in testing the equality of two slopes. In other words, we wish to determine if two given lines are statistically parallel. Let m 1 represent the regression coefficient for explanatory variable X 1 in sample 1 with size n 1 . Let m 2 represent the regression coefficient for X 2 in sample 2 with size n 2 . The difference between the two estimated slopes has the
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