ICA Chapter 6 Fall 2023

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University of Toledo *

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2600

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Statistics

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Feb 20, 2024

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In Class Activity – Chapter 6 Math 2600 Correlation Introduction to Statistics For this activity, we will analyze NFL team stats for the 2021 season. Specifically, we will compare two sets of variables to see which has the stronger correlation to the number of touchdowns: Cmp % (pass completion percentage) with TD (number of touchdowns) vs Pass Yds (number of passing yards) with TD (number of touchdowns). Keep in mind these numbers of over the entire football season. The data set below can also be accessed in Google Sheets . Team Cmp % Pass Yds TD 49ers 66.7 4437 26 Bears 61.2 3635 16 Bengals 69.2 4806 36 Bills 63.4 4450 36 Broncos 65.4 3856 20 Browns 61.5 3619 21 Buccaneers 67.3 5383 43 Cardinals 70.2 4619 27 Chargers 65.7 5014 38 Chiefs 66.4 4937 37 Colts 62.2 3588 27 Cowboys 68.6 4963 40 Dolphins 65.7 3936 21 Eagles 62.2 3585 20 Falcons 65.8 3987 20 Commanders 64.7 3746 21 Giants 59.2 3463 15 Jaguars 59.8 3674 12 Jets 59.2 3959 20 Lions 66.8 3884 23 Packers 67.8 4526 39 Panthers 58.1 3573 14 Patriots 68 4098 24 Raiders 68.3 4808 23 Rams 66.9 4893 41 Ravens 64.8 4267 21 Saints 58.1 3437 29 Seahawks 65.4 3815 30 Steelers 64 4017 23 Texans 64.8 3630 21 Titans 67.1 3745 22 Vikings 65.9 4450 34 a. Suppose the explanatory variable (X) is the Cmp % and the response variable (Y) is TD. What kind of correlation – increasing or decreasing – do you expect to see? Explain your response. - Increasing. b. Generate the scatterplot with the explanatory variable (X) as CMP % and the response variable (Y) as TD. Describe what you see in the scatterplot being sure to mention direction, strength and shape. StatCrunch Directions: How to Generate a ScatterPlot Page 1 of 2

In Class Activity – Chapter 6 Math 2600 Correlation Introduction to Statistics - Both Cmp% and TD are quantitative. From the scatter plot we see an increasing, weak to moderate, and linear association between the two variables. Go to Graph > Scatter Plot > Select your X variable and select your y variable > Compute! c. Generate a different scatterplot now where the explanatory variable (X) is the Pass Yds and the response variable (Y) is TD. Describe what you see in the scatterplot being sure to mention direction, strength and shape. - Both pass yds and TD are quantitative. By visualizing into two groups, we see increasing, moderate and linear trend with few outliers. d. Generate the correlation for both scenarios here and state the correlation values clearly. StatCrunch Directions: How to Generate Correlation Value Go to Stat > Summary Stat > Correlation > Select your two variables > Compute! - R (cmp% vs TD) = 0.55 r (pyd vs TD) = 0.80 e. Compare the scatterplots and correlation values from the two analyses. Which variable (Cmp % or Pass Yds) looks to have a stronger correlation with TD? Explain your answer. - r (cmp% vs TD) =0.55 changed to 0.61 when we removed the outliers. Comparing the r-values, we can say that pass yards look to have a stronger correlation with TD compared to cmp% with TD. Pass completion does not necessarily lead to TD where as passing yds has a higher chance of leading to TD. There may be a presence of a lurking variable like, fast runners, etc. Page 2 of 2

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