In Exercise 24, remove the data for the student who is 57 inch...

Question

In Exercise 24, remove the data for the student who is 57 inches tall and scored 128 on the IQ test. Describe how this affects the correlation coefficient r.

Accepted Answer

Hi, everyone. Let's take a look at our next problem. A researcher is studying the relationship between hours of weekly exercise and resting heart rate in beats per minute among a group of adults. The data per 48 participants is shown below. So we have a table where the first column is weekly exercise hours, or X, and the second column is resting heart rate or Y. So I'm going to read out the pairs of variables in each row. So, exercise hours and heart rate, 1 in 82, 2 and 78, 3 and 75, 4 and 72, 5 and 69, 6 and 66, 7 and 62, 8 and 58. Then we're told the correlation coefficient for the data is R equal to 0.99, indicating a strong negative linear relationship. More exercise is associated with a lower resting heart rate. The researcher decides to remove the data for the participant who exercised 1 hour per week and had a heart rate of 82. How would removing this data point most likely affect the correlation coefficient R? The value of r stays exactly the same because only one point was removed. The value of R becomes more negative, because removing data always strengthens the correlation. The value of r increases to 0 because the remove point caused all the variation. Or the value of r becomes slightly less negative because a data point that supported the trend was removed. So, let's recall what R is. R is a measure of the strength of the correlation between two variables. And we recall that that can go from 1 or -1, indicating the strongest possible correlation in 1 to 1 linear relationship, and zero indicating no correlation. So we know we have a very strong negative correlation. And so choice C, the value of R increases to zero because our move point caused all the variation, would not be our answer. We still have a strong correlation in our remaining. Values. And then we can also rule out choice A, the value of R stays exactly the same because only one point was removed. We wouldn't expect a big change, um, since only one point was removed, but R is based on these values, and so removing a very removing a value will change R, even if only slightly. Choice B says the value of R becomes more negative because removing data always strengthens the correlation. In multiple choice questions, be wary of words like always or never, and in this case, that we are wise to be wary, because removing data will not always strengthen the correlation. If you remove data that supports the trend. That will weaken your correlation. If you remove data that does not support the trend, it's an outlier that will strengthen the correlation. So, the answer is it depends on whether the data supports the trend. So choice be cannot be our answer. Then finally, choice D. We know this is the answer by elimination, but let's look at it. The value of DR becomes slightly less negative because the data point that supported the trend was removed. So, slightly less negative or called goes closer to zero, which is that by being not correlated. So this indicates a weaker. Correlation Because we did remove a data point that supported the trend. That data point was the lowest number of exercise hours and the highest resting heart rate. So, it won't have a large effect, but it did support the trend. It was another additional piece of data supporting it. So that's going to make our art just a little bit weaker. So once again, we're given this table showing these relationships between weekly exercise hours and heart rate. We're told the correlation coefficient is negative 0.99, and then told the researcher removes the first data point. And we're told, we're asked how removing that data point will most likely affect the correlation coefficient R. And our answer is choice D, the value of R becomes slightly less negative, because the data point that supported the trend was removed. See you in the next video.

In Exercise 24, remove the data for the student who is 57 inches tall and scored 128 on the IQ test. Describe how this affects the correlation coefficient r.

Key Concepts

Correlation Coefficient (r)

Outliers

Impact of Data Removal

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