Question

Which of the following is a true statement about residuals? Choose the correct answer below. 0 A. The regression line is the line that minimizes the standard deviation of the residuals. O B. The residual plot for a model that a good fit to the data should not show any pattern or have any unusual features. O C. A residual is the difference between the actual data value and the value predicted by the model 0 D. All of the above

Answer 1

Solution :

We have to find out which of the following statements is true for the Residuals !!

Statement of Option (A) :

*****The regression line is the line that minimizes the standard deviation of the residuals.*****

Explanation for Option (A) : We know that the Regression Line is constructed by estimating the values of the Intercept and the Slope , and this is done by minimising the Sum of Squares of the Residuals which is actually the Square of the Standard Deviation of the Residuals. Thus , we can say that , Option (A) is partially correct.

Statement of Option (B) :

*****The residual plot for a model that a good fit to the data should not show any pattern or have any unusual features*****

Explanation for Option (B) : We know that the Residual Plot is a Graphical Representation that plots the Residuals in the Y - axis and the Explanatory (Independent) variable in the X - axis , and , further if the points in the Residual Plot are randomly dispersed or do not show any kind of pattern , then we can say that the Regression Model is good fit to the data. Thus , Option (B) is Correct.

Statement of Option (C) :

*****A residual is the diff. b/w the actual data value and the value predicted by the model*****

Explanation for Option (C) : Again , we know that a Residual is nothing but the difference between the Observed (Actual) data values and the Predicted Values that are estimated by the Regression Model. Thus , we can say that , Option (C) is also Correct.

As mentioned earlier , Option (A) is partially correct but , according to the question given , if two options are correct , then all answers should be correct. That is , the Correct Option should Option (D) All of the Above..........................(Ans)

______________________________________________