If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate?
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A. B. C. D. E.Explanation
The standard error of estimate basically measures the difference between the points and the straight line.
In a scatter diagram, the standard error of estimate measures the accuracy of the regression line in predicting the dependent variable (Y) based on the independent variable (X). It represents the average distance between the observed data points and the predicted values on the regression line.
If all the plots on a scatter diagram lie on a straight line, it indicates a perfect linear relationship between the variables. In this case, the regression line perfectly fits the data points, and there is no variation or error between the observed values and the predicted values. Therefore, the standard error of estimate would be zero (option C).
Option A, infinity, is incorrect because when the data points lie on a straight line, there is no infinite error involved. Instead, the error is minimized.
Option B, none of these answers, is incorrect because there is a valid answer available.
Option D, +1, and option E, -1, are incorrect because the standard error of estimate is a measure of accuracy, and it is not represented by a single value of +1 or -1. It is a numerical value that represents the dispersion of data points around the regression line.
Therefore, the correct answer is option C, 0, indicating that there is no standard error of estimate when all the plots on a scatter diagram lie on a straight line.