Question

In a simple linear regression model, if the independent and dependent variables are negatively linearly related, then the standard error of the estimate will also be negative.

Answer 1

No, standard error will not be negative

Standard error of the regression, also known as the standard error of the estimate. The standard error of the regression provides the absolute measure of the typical distance that the data points fall from the regression line.

standard error=sqrt(Mean Square Error)=sqrt(Sum of Square Error/df)

so standard error is the square root of sum of square and sum of square is always positive.

so standard error will be always positive .