If a simple linear regression model is developed based on a sample where the independent and dependent variables are known to be negatively related, then the sum of squares for error will be negative also.

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Quizplus · Accepted Answer

The sum of squares for error cannot be negative by definition. It is the sum of the squared differences between the actual values and the predicted values, and these differences cannot be negative. If the regression model is developed based on a sample where the independent and dependent variables are known to be negatively related, then the slope coefficient of the regression line will be negative and the sum of squares for error will be positive.

If a Simple Linear Regression Model Is Developed Based on a Sample