Question

Following the debut of the new SAT Writing test in March $2005$, Dr. Les Perelman from the Massachusetts Institute of Technology collected data from a set of sample essays provided by the College Board. A least-squares regression analysis was performed on these data. The two graphs below display the results of that analysis. Explain why the conditions for performing inference are not met in this setting.

Short answer

Linear and Equal variance condition have not been met.

Step-by-step solution

Given information

The given data is

Explanation

The five prerequisites for performing inference using least-squares regression analysis are random, normal, independent, equal variance, and linear.

The Linear condition is not satisfied since both the scatterplot and the residual plot have a curvature.

The Equal variance criteria is also not met because the vertical spread between the points in the residual plot is greater to the left than it is to the right.

The requirements of linearity and equal variance have not been met.