Chapter 2, XXXXXXXXXXSection 5, Exercise 162 With XXXXXXXXXXwhich of the following scatterplots below does the correlation,r=0.8, match? \ a. Scatterplot (a) b. Scatterplot (b) c. Scatterplot...

With which of the following scatterplots below does the correlation,r=0.8, match?

\

With which of the following scatterplots below does the correlation,r=-0.38, match?

Two quantitative variables are described below. Do you expect a positive or negative association between the two variables?
Size of a houseandCost to heat the house

Two quantitative variables are described below. Do you expect a positive or negative association between the two variables?
Amount of time spent studyingandGrade on the exam

Choose the scatterplot of the data below. Put theXvariable on the horizontal axis and theYvariable on the vertical axis.

UseStatKeyor other technology to find the correlation for the following data.

Clickhereto accessStatKey.
Round your answer to three decimal places.
The correlation isr=Enter your answer in accordance to the question statement
^*1
.

Significant digits not applicable; the absolute tolerance is +/-0.001

Mother's Love, Hippocampus, and Resiliency

Multiple studies¹in both animals and humans show the importance of a mother's love (or the unconditional love of any close person to a child) in a child's brain development. A recent study shows that children with nurturing mothers had a substantially larger area of the brain called the hippocampus than children with less nurturing mothers. This is important because other studies have shown that the size of the hippocampus matters: People with large hippocampus area are more resilient and are more likely to be able to weather the stresses and strains of daily life. These observations come from experiments in animals and observational studies in humans.

¹Raison, C., "Love key to brain development in children," cnn.com,The Chart, March 12, 2012.

(a) Is the amount of maternal nurturing one receives as a child positively or negatively associated with hippocampus size?

(b) Is hippocampus size positively or negatively associated with resiliency and the ability to weather the stresses of life?

(c) Can we conclude that maternal nurturing in humans causes the hippocampus to grow larger?

Can we conclude that maternal nurturing in animals (such as mice, who were used in many of the experiments) causes the hippocampus to grow larger?

Social Jetlag

Social jetlag refers to the difference between circadian and social clocks, and is measured as the difference in sleep and wake times between work days and free days. For example, if you sleep between11pm and7am on weekdays but from2am to10am on weekends, then your social jetlag is three hours, or equivalent to flying from the West coast of the US to the East every Friday and back every Sunday. Numerous studies have shown that social jetlag is detrimental to health. One recent study¹measured the self-reported social jetlag of145healthy participants, and found that increased social jetlag was associated with a higher BMI (body mass index), higher cortisol (stress hormone) levels, higher scores on a depression scale, fewer hours of sleep during the week, less physical activity, and a higher resting heart rate.
(a) Indicate whether social jetlag has a positive or negative correlation with each variable listed: BMI, cortisol level, depression score, weekday hours of sleep, physical activity, heart rate.
BMI:

Cortisol level:

Depression score:

Weekday hours of sleep:

Physical activity:

Heart rate:

(b) Can we conclude that social jetlag causes the adverse effects described in the study?

¹Rutters F, et al., "Is social jetlag associated with an adverse endocrine, behavioral, and cardiovascular risk profile?"J Biol Rhythms, 2014 October; 29(5); 377-83.

NFL Pre-Season

Does pre-season success indicate regular season success in the US National Football League? We looked at the number of pre-season wins and regular season wins for all 32 NFL teams over a 10 year span.

(a) What would a positive association imply about the relationship between pre-season and regular season success in the NFL?

(b) What would a negative association imply about the relationship between pre-season and regular season success in the NFL?

(c) The correlation between these two variables isr=0.067. What does this correlation tell you about the strength of a linear relationship between these two variables?

Genetic Diversity and Distance from Africa

It is hypothesized that humans originated in East Africa, and migrated from there. We compute a measure of genetic diversity for different populations,⁶⁶and the geographic distance of each population from East Africa (Addis Ababa, Ethiopia), as one would travel over the surface of the earth by land (migration long ago is thought to have happened by land). The relationship between these two variables is shown in the figure below and the data are given inGeneticDiversity.

¹Calculated from data from S Ramachandran, O Deshpande, CC Roseman, NA Rosenberg, MW Feldman, LL Cavalli-Sforza.

(a) Describe the relationship between genetic diversity and distance from East Africa. Does there appear to be an association?

If so, it is positive or negative?

Strong or weak?

Linear or nonlinear?

(b) Which of the following values gives the correlation between these two variables?

(c) On which continent is the population with the lowest genetic diversity?

(d) On which continent is the population that is farthest from East Africa (by land)?

(e) Populations with greater genetic diversity are thought to be better able to adapt to changing environments, because more genetic diversity provides more opportunities for natural selection. Based only on this information and the given figure, do populations closer or farther from East Africa appear to be better suited to adapt to change?

Exercising or Watching TV?

TheStudentSurveydataset includes information on the number of hours a week students say they exercise and the number of hours a week students say they watch television.

Number of hours a week of exercise and of television watching

Clickherefor the dataset associated with this question.

(a) There are two outliers in this scatterplot.
Describe the student corresponding to the outlier on the right.

Describe the student corresponding to the outlier on the top.

(b) The correlation between these two variables isr=0.01. What does this correlation tell you about the strength of a linear relationship between these two variables?

Iris Petals

Allometry is the area of biology that studies how different parts of a body grow in relation to other parts. The figure below shows a scatterplot¹comparing the length and width of petals of irises.

Iris petals

¹R.A. Fishers's iris data downloaded from http://lib.stat.cmu.edu/DASL/Datafiles/Fisher'sIrises.html.

(a) Does there appear to be a positive or negative association between petal width and petal length?

(b) Estimate the correlation.

(c) Estimate the width of the petal which has a length of30mm.
Round your answer to the nearest integer.
petal width≈
^*1
mm

Significant digits not applicable; the absolute tolerance is +/-1

(d) There are at least two different types of irises included in the study. Name one difference between the types that the scatterplot makes obvious.

UseStatKeyor other technology to find the regression line to predictYfromXusing the following data.

Clickhereto accessStatKey.
Round your answers to three decimal places.
The regression equation isY^=
^*1
+
^*2
X.

^*1

- significant digits not applicable; the absolute tolerance is +/-0.001



^*2

- significant digits not applicable; the absolute tolerance is +/-0.001

Is It Getting Harder to Win a Hot Dog Eating Contest?

Every Fourth of July, Nathan’s Famous in New York City holds a hot dog eating contest. The table below shows the winning number of hot dogs and buns eaten every year from 2002 to 2015, and the data are also available inHotDogs. The figure below shows the scatterplot with the regression line.

Winning number of hot dogs in the hot dog eating contest

Winning number of hot dogs and buns

Clickherefor the dataset associated with this question.
Clickhereto accessStatKey.

(a) Is the trend in the data mostly positive or negative?

(b) Using the figure provided, is the residual larger in 2007 or 2008?
Choose the answer from the menu in accordance to item (b) of the question statement

Is the residual positive or negative in 2010?
Choose the answer from the menu in accordance to item (b) of the question statement

(c) UseStatKeyor other technology to find the correlation.
Round your answer to three decimal places.
r=Enter your answer in accordance to the question statement
^*1

Significant digits not applicable; the absolute tolerance is +/-0.001

(d) UseStatKeyor other technology to find the regression line to predict the winning number of hot dogs from the year.
Round your answer for the intercept to the nearest integer and your answer for the slope to two decimal places.
HotDogs^=Enter your answer in accordance to item (d) of the question statement
^*1
+Enter your answer in accordance to item (d) of the question statement
^*2
(Year)

^*1

- significant digits not applicable; the absolute tolerance is +/-1



^*2

- significant digits not applicable; the absolute tolerance is +/-0.01

(e) Interpret the slope of the regression line.

(f) Predict the winning number of hot dogs in 2016.
Round your answer to the nearest integer.
HotDogs^=Enter your answer in accordance to the question statement
^*1

Significant digits not applicable; the absolute tolerance is +/-20

Football and Cognitive Percentile

A recent study¹examined several variables on collegiate football players, including the variableYears, which is number of years playing football, and the variablePercentile, which gives percentile on a cognitive reaction test. The regression line for predictingPercentilefromYearsis:

P⁢e⁢r⁢c⁢e⁢n⁢t⁢i⁢l⁢e^=102-3.34⋅Y⁢e⁢a⁢r⁢s.

¹Singh R, et al., "Relationship of Collegiate Football Experience and Concussion with Hippocampal Volume and Cognitive Outcomes",JAMA, 311(18), 2014. Data values are estimated from information in the paper.

(a) Predict the cognitive percentile for someone who has played football for8years and for someone who has played football for17years.
Enter the exact answers.
The cognitive percentile for someone who has played football for8years is
^*1
.
The cognitive percentile for someone who has played football for17years is
^*2
.

^*1

- significant digits not applicable; exact number, no tolerance



^*2

- significant digits not applicable; exact number, no tolerance

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

(c) All the participants had played between7and18years of football. Is it reasonable to interpret the intercept in context?