The question asks whether influential observations typically exist when the point is an outlier relative to the values of the explanatory variable.

Explanation:

In statistics, an influential observation is a data point that has a significant impact on the regression line, meaning it can substantially change the slope or direction of the line. Often, influential points are outliers, particularly in the horizontal direction (i.e., in terms of the explanatory variable).

An outlier in terms of the explanatory variable is far from the bulk of the data points along the x-axis. Such outliers can pull the regression line toward themselves, which makes them influential.

Conclusion:

Since influential points are often outliers with respect to the explanatory variable, the statement is True.

Would you like more details on outliers and influential observations?

Follow-up Questions:

1. What is the difference between an outlier and an influential observation?
2. How do you detect an influential point in regression analysis?
3. What are some methods to reduce the effect of influential observations?
4. Can an outlier in the response variable be influential?
5. How does the Cook’s distance help in identifying influential observations?

Tip:

In regression analysis, not all outliers are influential. Always analyze whether a point significantly affects the overall fit.