Final answer:
A classifier/decision boundary nearly parallel to the y-axis means the x variable has little impact on y, indicating a weak or non-existent linear relationship, suggesting x may not be a good predictor for y in linear regression.
Step-by-step explanation:
When a classifier/decision boundary in a two-dimensional space is nearly parallel to the horizontal y-axis, it implies that the value of the y variable does not depend significantly on the x variable in the classification or regression analysis. In the context of linear regression, a decision boundary parallel to the y-axis suggests that changes in x have little to no effect on the y variable, resulting in an insignificant linear relationship between x and y. If the goal is to use the regression line to model the relationship between x and y, having a nearly vertical decision boundary indicates that the x variable may not be a good predictor for the y variable.
When analyzing the pattern in a scatter plot to decide if x and y are suitable for linear regression, as we see in items #11 and #12, the angle of the decision boundary relative to the axes is a key factor. If the scatter plot shows a collection of points with no clear pattern or a pattern that leads to a vertical line when attempting to fit a linear regression model, this denotes that the variables may not have a meaningful linear relationship and might not be good candidates for linear regression.