Question

Suppose a researcher collects data on the pollen allergen levels, measured in grains per cubic meter, in the morning and evening

in 35 cities. The data is plotted with morning pollen allergen levels on the horizontal axis and evening pollen allergen levels on
the vertical axis. Dayton, Ohio is an outlier in the x-direction.
What must be true about this city? Select all true statements.
The absolute value of the residual of this city is large.
The evening pollen allergen levels for this city are much higher or lower than other cities in the data set that have
similar morning pollen allergen levels.
This city is an influential observation.
The morning pollen allergen levels for this city are much higher or lower than the rest of the cities in the data set.
The evening pollen allergen levels for this city are much higher or much lower than the rest of the cities in the data set.

Answer 1

Dayton, Ohio is an outlier in the x-direction with morning pollen allergen levels much higher or lower than other cities in the data set. The evening pollen allergen levels for this city may or may not be much higher or lower than cities with similar morning levels. The absolute value of the residual for this city is large.

Step-by-step explanation:

Dayton, Ohio is an outlier in the x-direction, which means that its morning pollen allergen levels are much higher or lower than the rest of the cities in the data set. Therefore, the statement 'The morning pollen allergen levels for this city are much higher or lower than the rest of the cities in the data set' is true.

However, since we do not have information about the evening pollen allergen levels for this city, we cannot determine if the evening levels are much higher or lower than other cities with similar morning levels. So, the statement 'The evening pollen allergen levels for this city are much higher or lower than other cities in the data set that have similar morning pollen allergen levels' may or may not be true.

The statement 'The absolute value of the residual of this city is large' is also true because an outlier in the x-direction will have a large absolute value of the residual. On the other hand, we cannot determine if this city is an influential observation without more information about its impact on the regression model.

Learn more about outliers in scatterplots