The RMSE of a line with slope 0 and intercept of the mean of y is said to be equal to the same as the standard deviation of the variable y.
So when the slope is said to be zero, the RMSE will be e = equal to the standard deviation of the variable y.
In cases of standardized observations and forecasts that are said to be used as RMSE inputs, there found to be a direct association with the correlation coefficient.
So For example, when the correlation coefficient is said to be 1, the RMSE will then be 0, due to the fact that all of the points can be seen *(lie) on the regression line.
Therefore, So when the slope is said to be zero, the RMSE will be e = equal to the standard deviation of the variable y.
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See full question below
What is the RMSE of a line with slope 0 and intercept of the mean of y equal to? RMSE is short for root mean squared error.
Hint 1: The line with slope 0 and intercept of mean of y is just a straight horizontal line at the mean of y
Hint 2: What does the formula for RMSE become if we input our predicted y values in the formula. Try writing it out on paper!
