In Exercise 26, add data for an international soccer player wh...

Question

In Exercise 26, add data for an international soccer player who can perform the half squat with a maximum of 210 kilograms and can sprint 10 meters in 2.00 seconds. Describe how this affects the correlation coefficient r.

Accepted Answer

Hello, everyone, and welcome back. Glad to have you with us. The next problem is a strength coach strength coach is studying the relationship between an athlete's maximum half squat load in kilograms and their 10 m sprint time in seconds. The data for 8 athletes is shown below. What column 1 says max, half squat in kilograms. Column 2 says print time in seconds. So I'll read the corresponding data. So 130, 2.35, 140, 2.28, 150, 2.2, 160, 2.12, 170, 2.05, 180, 1.98, 190, 1.91, 200, 1.85. The correlation coefficient for this data is R equal to 0.99, indicating a strong negative linear relationship. Higher squat strength is associated with faster sprint times. Now, the coach adds data for a new athlete who squats 210 kg and has a sprint time of 2.00 seconds. How will this affect the correlation coefficient are? The value of R becomes more negative, because the new athlete is stronger than the others. The value of r becomes less negative since the added point weakens the negative linear relationship. See the value of R increases to 0, since the new data point overrides the existing trend. Or the value of R remains unchanged because adding one point does not affect the correlation. So two of these we can eliminate quite easily. Choice C, the value of R increases to 0. Recall that zero means no correlation whatsoever. So even if the new data point goes against the existing trend, it isn't going to completely eliminate 7 other data points that have this strong negative linear relationship. So We'll say that C is incorrect because the other data points are still strongly correlated. In choice D, the value of R remains unchanged because adding one point does not affect the correlation. Well, this is incorrect. Uh, one point might not have a huge effect on R, but all the data points are part of its calculation. Changing one will change R even if only slightly. So, we need to look at A and B. Does R become more or less negative? Well, recall that R indicates the strength of the linear relationship with positive 1 and negative 1 being 1 to 1 linear relationships, so the strongest possible, and zero indicating no relationship whatsoever. So since our R is negative, the value of R becoming more negative would indicate a stronger. Correlation as a result of the new data. And are becoming less negative would indicate a weaker correlation. As a result of the new data. So, let's see how the data compares. So again, we see in general that as the squat. Amount increases, the sprint time decreases. So the data that will be added is an athlete who squats 210 kg, so higher than anyone else here, and that is a sprint time of 2.00 seconds. But that's down in the lower range of sprint times. So that new data point will be an outlier here. It does not support the trend that we see in the other values. So that would lead to a weaker correlation, so less negative, so choice B, and since this added point weakens that negative linear relationship. And then we'll cross out choice. A, the value of R does not become more negative, because this new athlete is not stronger than the others. So, again, we have this table of values, and they show a strong negative linear relationship. We're adding a data point that's an outlier and asked how that affects our correlation coefficient, and the answer is B. That value of R becomes less negative since the added point weakens the negative linear relationship. See you in the next video.

In Exercise 26, add data for an international soccer player who can perform the half squat with a maximum of 210 kilograms and can sprint 10 meters in 2.00 seconds. Describe how this affects the correlation coefficient r.

Key Concepts

Correlation Coefficient (r)

Half Squat Performance

Sprinting Speed

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