ɪf the regresion coefficient is the coefficient of determination, then it's range is between 0 or 1. ɪf the regression coefficient is the correaltion coefficient (which i think it is) the it must lie between -1 or 1.
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8.7.4 Properties of Regression Coefficients:(a) Correlation coefficient is the geometric mean between the regression coefficients. (b) If one of the regression coefficients is greater than unity, the other must be less than unity.(c) Arithmetic mean of the regression coefficients is greater than the correlation coefficient r, providedr > 0.(d) Regression coefficients are independent of the changes of origin but not of scale.
The coefficient, also commonly known as R-square, is used as a guideline to measure the accuracy of the model.
The correlation coefficient is symmetrical with respect to X and Y i.e.The correlation coefficient is the geometric mean of the two regression coefficients. or .The correlation coefficient lies between -1 and 1. i.e. .
That is not true. It is possible for a data set to have a coefficient of determination to be 0.5 and none of the points to lies on the regression line.
It's not quite possible for the coefficient of determination to be negative at all, because of its definition as r2 (coefficient of correlation squared). The coefficient of determination is useful since tells us how accurate the regression line's predictions will be but it cannot tell us which direction the line is going since it will always be a positive quantity even if the correlation is negative. On the other hand, r (the coefficient of correlation) gives the strength and direction of the correlation but says nothing about the regression line equation. Both r and r2 are found similarly but they are typically used to tell us different things.