Question

Are hot dogs that are high in calories also high in salt? The following scatterplot shows the calories and salt content (measured in milligrams of sodium) in 17 brands of meat hot dogs.

What effect does the hot dog brand with the smallest calorie content have on the correlation? Justify your answer.

A) The hot dog with the lowest calorie content decreases the correlation. It does not fall in the linear pattern of the rest of the data.

B) The hot dog with the lowest calorie content increases the correlation. It does not fall in the linear pattern of the rest of the data.

C) (INCORRECT) The hot dog with the lowest calorie content does not change the correlation. It falls in the linear pattern of the rest of the data.

D) The hot dog with the lowest calorie content increases the correlation. It falls in the linear pattern of the rest of the data.

E) The hot dog with the lowest calorie content does not change the correlation. It does not fall in the linear pattern of the rest of the data.

Answer 1

The hot dog with the lowest calorie content likely decreases the correlation if it doesn't fall within the linear pattern of the rest of the data, thus behaving as an outlier and skewing the correlation coefficient.

Therefore, the correct answer is:

A) The hot dog with the lowest calorie content decreases the correlation. It does not fall in the linear pattern of the rest of the data.

Step-by-step explanation:

The influence of the hot dog brand with the smallest calorie content on the correlation can be determined by examining its position in relation to the overall pattern of the scatterplot.

When such a point does not follow the linear pattern observed among the rest of the data, it can have an effect on the calculation of the correlation coefficient.

In this context, if the hot dog with the lowest calorie content doesn't fit the overall linear trend of calories versus salt content, it would be considered an outlier.

Outliers can skew the correlation coefficient by stretching the pattern of the data. If the hot dog with the smallest calorie content is significantly lower in calories compared to others but its salt content isn't correspondingly low or high to maintain the trend, it would decrease the correlation because it doesn't fall within the expected linear relationship between calories and sodium content.

Therefore, the correct answer is:

A) The hot dog with the lowest calorie content decreases the correlation. It does not fall in the linear pattern of the rest of the data.