Question

Hot dogs Are hot dogs that are high in calories and 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.

a. The correlation for these data is $r=0.87$ Interpret this value.

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

Short answer

Part (a) There is a fairly strong and positive association between the calories and sodium in $17$brands of meat hot dogs.

Part (b) The linear correlation coefficient would increase.

Step-by-step solution

Part (a) Step 1: Given information

Correlation, r = 0.87

Part (a) Step 2: Explanation

A positive linear correlation exists when $r$ is positive.

A negative linear correlation exists when $r$ is negative.

For weak correlation,

$0<\left|r\right|<0.5$

For moderate correlation,

$0.5<\left|r\right|<0.8$

For strong correlation,

$0.8<\left|r\right|<1$

Note that

The association between the calories and sodium in $17$ brands of meat hot dogs is a strong and positive association.

Part (b) Step 1: Explanation

Note that

The point with the lowest calorie content in the scatterplot does not follow the general linear pattern of the other data points.

Thus,

When this point is removed from the data collection, the data seems to be more linear.

Hence,

There will be an increase in the linear correlation coefficient.