Question

_{Regression If the methods of this section are used with paired sample data, and the conclusion is that there is sufficient evidence to support the claim of a correlation between the two variables, can we use the methods of Section 10-2 to find the regression equation that can be used for predictions? Why or why not?}

Short answer

No, the methods of Section 10-2 should not be used to compute the regression equation for the given paired data as the regression equation is based on a linear correlation between the two variables. However, the method of rank correlation coefficient does not indicate whether the correlation between the two variables is linear or not.

Step-by-step solution

Given information

For a given set of data, the correlation between the two variables is obtained to be significant using the rank correlation method.

The regression equation is obtained for prediction purposes.

Define regression equation

The regression equation between the two variables that can be used for predictions is based on the linear correlation between the variables.

Define rank correlation test

The rank correlation test, if it turns out to be significant, indicates that there is a correlation between the two variables. However, it does not necessarily determine whether the correlation is linear or not linear.

Regression vs.rank correlation

Although the correlation emerges to be significant using the rank correlation test, it cannot be decisively concluded whether the correlation is linear or not as it may indicatea non-linear relationship between paired set of ordinal values.

Thus, the regression equation between the two variables cannot be used for prediction as the regression equation necessarily involves the existence of a linear correlation between the two variables.

Therefore, it can be said that the regression method of Section 10-2 would not be considered as a suitable method in order to make predictions in this section.