Question

The sum of the difference between the actual values of $Y$ and its values obtained from the fitted regression line is always:

• A. Zero
• B. Positive
• C. Negative
• D. Minimum

Answer 1

The correct option is A Zero

Let the actual values be $y_1,y_2,...,y_n$

Let the values obtained from the fitted regression analysis be ${\hat{y}}_1,{\hat{y}}_2,...,{\hat{y}}_n$

Since, the values are obtained from the fitted regression line.

Therefore, the actual and obtained values are almost equal.

Therefore, $y_1={\hat{y}}_1$, $y_2={\hat{y}}_2$ , ... , $y_n={\hat{y}}_n$

sum of the difference between the actual and obtained values is $(y_1-{\hat{y}}_1)+(y_2-{\hat{y}}_2)+...+(y_n-{\hat{y}}_n)=0$