Question

If all the actual and estimated values of $Y$ are same on the regression line, the sum of squares of error will be:

• A. Zero
• B. Minimum
• C. Maximum
• D. Unknown

Answer 1

Answer: (A)

Zero

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

Let the estimated values be ${\hat{y}}_1,{\hat{y}}_2,...,{\hat{y}}_n$

Error is $actual-estimated$

Given that actual and estimated values are equal.

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

sum of squares of error is $(y_1-{\hat{y}}_1{)}^2+(y_2-{\hat{y}}_2{)}^2+...+(y_n-{\hat{y}}_n{)}^2=0$