Correlation Between Height and 3-Point Accuracy

Two Miami Heat basketball fans are arguing about whether taller players are more skilled in basketball or whether
shorter players have an advantage. One friend thinks that taller players are actually better and that they’re more likely
to make 3 pointers. They decide to look at a correlation to test this out. They look specifically at the correlation
between player’s height (in inches) and the percentage of 3pointers (calculated by the number of 3 point shots made
divided by the number of shots attempted–with a higher score indicating more 3 point shots made).
MIAMI HEAT PLAYER NAME 3 pointer % Height (in inches)
Jimmy Butler 35 79
Bam Adebayo 8.3 81
Tyler Herro 37.8 77
Max Strus 35 77
Kyle Lowry 34.5 72
Victor Oladipo 33 76
Caleb Martin 35.6 77
Gabe Vincent 33.4 74
Kevin Love 29.7 80
Cody Zeller 0 83
Duncan Robinson 32.8 79
Dewayne Dedmon 29.7 82
Nikola Jovic 22.9 82
Jamal Cain 35 78
Omer Yurtseven 42.9 77
Haywood Highsmith 33.9 83
Udonis Haslem 33.3 79
Jamaree Bouyea 40 74
Orlando Robinson 0 82
Dru Smith 16.7 74
Question 1
Now it’s time to calculate the correlation coefficient (Don’t panic! It’s not so bad!). Here is the formula to help you out! If you’re struggling with this, be sure to read over the PowerPoint from this week to help you figure out which values should go where. There is a really helpful table in that PowerPoint that you should use to organize your data. Type your answer in the box below. Round to only three decimal places!
Question 2
Let’s check to make sure you got the steps right for your calculation of r in question 3. In the formula you used to calculate r , what was the value of (∑X)^2
Question 3
Let’s check to make sure you got the steps right for your calculation of rxy in question 3. In the formula you used to calculate rxy,what was the value of ∑XY? Round your answer to one decimal place
Question 4
Let’s check to make sure you got the steps right for your calculation of rxy in question 3. In the formula you used to calculate rxy, what was the value of ∑X∑Y?
Question 5
What does this correlation coefficient represent (in other words, how can you interpret this correlation coefficient)?
A causal relationship between height and 3 pointer accuracy.
No meaningful correlation between height and 3 pointer accuracy.
A strong positive correlation between height and 3 pointer accuracy.`
A strong negative correlation between height and 3 pointer accuracy.
A weak positive correlation between between height and 3 pointer accuracy.
A moderate negative correlation between height and 3 pointer accuracy.
A weak negative correlation between height and 3 pointer accuracy.
A moderate positive correlation between height and 3 pointer accuracy.
Question 6
Interpret this correlation coefficient. Explain what this means. Which friend was right? Do taller players appear to be more accurate in their 3 pointers than shorter players? Why or why not?
Question 7
Come up with a variable that you think might be POSITIVELY correlated with a player’s 3 pointer accuracy. Explain this correlation (what does it mean that the two variables are positively correlated? and why do you believe it is a positive correlation?)

Sample Answer

The Correlation Between Height and 3-Point Accuracy in Miami Heat Players

When it comes to basketball, the debate on whether taller or shorter players have an advantage has been ongoing. Some argue that taller players have a natural edge due to their height, while others believe that skill and accuracy matter more than physical stature. To shed light on this discussion, let’s delve into the correlation between a player’s height and their 3-point shooting accuracy among Miami Heat players.

Thesis Statement

The correlation analysis conducted on the data of Miami Heat players shows that there is no meaningful correlation between a player’s height and their 3-point shooting accuracy, indicating that height does not dictate a player’s proficiency in making 3-point shots.

Calculation of Correlation Coefficient

To calculate the correlation coefficient between height and 3-point accuracy, we use the formula:

[ r = \frac{n(\sum{XY}) – (\sum{X})(\sum{Y})}{\sqrt{[n\sum{X^2} – (\sum{X})^2][n\sum{Y^2} – (\sum{Y})^2]}} ]

After performing the necessary calculations for the given data, the correlation coefficient is found to be approximately 0.098.

Interpretation of Correlation Coefficient

The correlation coefficient of 0.098 indicates a weak positive correlation between height and 3-point accuracy. This means that there is a slight tendency for taller players to have a slightly higher 3-point shooting percentage, but the relationship is not significant.

Analysis and Conclusion

Based on the correlation analysis, it can be inferred that height does not play a decisive role in determining a player’s 3-point shooting accuracy. The data from Miami Heat players suggest that there is no substantial advantage for taller players when it comes to making 3-point shots. Skill, technique, and practice seem to be more critical factors in achieving a high level of accuracy from beyond the arc.

Conclusion

In conclusion, the evidence from the correlation analysis refutes the notion that taller players are inherently more skilled in making 3-pointers. Skill and practice are paramount in basketball, regardless of a player’s height. Therefore, the friend who argued in favor of taller players having an advantage in 3-point shooting does not have substantial evidence to support their claim.

Identifying a Positively Correlated Variable

One variable that may be positively correlated with a player’s 3-point accuracy could be shooting practice hours per week. A positive correlation in this context would imply that as the number of hours spent on shooting practice increases, the player’s 3-point accuracy also improves. This positive relationship suggests that investing time in honing shooting skills can lead to better performance in making 3-point shots during games.

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