A regression equation is obtained for the following set of data. $\begin{array} { r | r r r r r r } \mathrm { x } & 2 & 4 & 6 & 9 & 10 & 12 \ \hline \mathrm { y } & 28 & 33 & 39 & 45 & 47 & 52 \end{array}$
For what range of x-values would it be reasonable to use the regression equation to predict the y-value corresponding to a given x-value? Why?

Question

A regression equation is obtained for the following set of data. $\begin{array} { r | r r r r r r }  \mathrm { x } & 2 & 4 & 6 & 9 & 10 & 12 \ \hline \mathrm { y } & 28 & 33 & 39 & 45 & 47 & 52 \end{array}$  
For what range of x-values would it be reasonable to use the regression equation to predict the y-value corresponding to a given x-value? Why?

Quizplus · Accepted Answer

The Answer is It would be reasonable to use the regression equation to predict the y-value corresponding to a given x-value for x-values in the range from 2 to 12. We can reasonably use the regression equation to make predictions for values of the predictor variable (x)within the range of the observed values of the predictor value, in this case from 2 to 12. However, to do so for values of the predictor variable outside that range may not be reasonable, because the linear relationship between the variables may not hold there. Using the regression equation to make predictions for values of the predictor variable outside the range of the observed values of the predictor variable is called extrapolation. Grossly incorrect predictions can result from extrapolation. (Explanations will vary.)

A Regression Equation Is Obtained for the Following Set of Data