Football and Cognitive Percentile Exercise 2.143 on page 102 introduces a study that examines several variables on collegiate football players, including the variable Years, which is number of years playing football, and the variable Cognition, which gives percentile on a cognitive reaction test. Exercise 2.182 shows a scatterplot for these two variables and gives the correlation as -0.366 . The regression line for predicting Cognition from Years is:

\[\widehat{\text { Cognition }}=102-3.34 \cdot \text { Years }\]

(a) Predict the cognitive percentile for someone who has played football for 8 years and for someone who has played football for 14 years.

(b) Interpret the slope in terms of football and cognitive percentile.

(c) All the participants had played between 7 and 18 years of football. Is it reasonable to interpret the intercept in context? Why or why not?

Data From Exercise 2.143:
Football and Brain Size A recent study examined the relationship of football and concussions on hippocampus volume in the brain. The study included three groups with \(n=25\) in each group: heathy controls who had never played football, football players with no history of concussions, and football players with a history of concussions. Figure 2.41 shows side-by-side boxplots for total hippocampus volume, in \(\mu \mathrm{L}\), for the three groups.

Data From Exercise 2.182:
Exercise 2.143 on page 102 introduces a study that examines the association between playing football, brain size as measured by left hippocampal volume (in \(\mu \mathrm{L}\) ), and percentile on a cognitive reaction test. Figure 2.56 gives two scatterplots. Both have number of years playing football as the explanatory variable while Graph

(a) has cognitive percentile as the response variable and Graph

(b) has hippocampal volume as the response variable.

Figure 2.56:

Transcribed Image Text:

Total Hippocampus Volume 10000 9000 8000 7000 6000 5000 4000 Control Football No Concussion Football With Concussion Group Figure 2.41 Relationship of football and concussions on brain hippocampus size