The diagram below illustrates the confounding between

This preview shows page 31 - 34 out of 40 pages.

The diagram below illustrates the confounding between exposure to chemicals andstanding up.For 2.140Chemical exposureTimestanding up??MiscarriagesFor 2.141Seriousnessof illnessHospitalsizeLength ofstay2.141.Patients suffering from more serious illnesses are more likely to go to larger hospitals(which may have more or better facilities) for treatment. They are also likely to requiremore time to recuperate afterwards.
Solutions1192.142.Spending more time watching TV means thatlesstime is spent on other activities; thismay suggest lurking variables. For example, perhaps the parents of heavy TV watchers donot spend as much time at home as other parents. Also, heavy TV watchers would typicallynot get as much exercise.2.143.In this case, there may be a causative effect, but in the direction opposite to the onesuggested: People who are overweight are more likely to be on diets and so choose artificialsweeteners over sugar. (Also, heavier people are at a higher risk to develop diabetes; if theydo, they are likely to switch to artificial sweeteners.)2.144. (a)Statements such as this typically mean that the risk of dyingat a given ageis halfas great; that is, given two groups of the same age, where one group walks and the otherdoes not, the walkers are half as likely to die in (say) the next year.(b)Men who chooseto walk might also choose (or have chosen, earlier in life) other habits and behaviors thatreduce mortality.2.145.This is an observational study—students choose their “treatment” (to take or not takethe refresher sessions).2.146. (a)Time plot on the right.(b)The re-gression equation isˆy=11677957.83x.(c)The plot shows a clear negative associ-ation, and the slope of the regression linesays that the rank is decreasing at an averagerate of about 58 per year. Because alowerrank meanshigherpopularity, this meansthat “Atticus” is getting more popular.6006507007508008509009502003200420052006200720082009Rank of “Atticus”Year2.148. (a)The scatterplot shows a positive, curved relationship.(b)The regression explainsaboutr2.=98.3% of the variation in salary. While this indicates that the relationship isstrong, andcloseto linear, we can see from that scatterplot that the actual relationship iscurved.2.149. (a)The residuals are positive at the beginning and end, and negative in the middle.(b)The behavior of the residuals agrees with the curved relationship seen in Figure 2.30.2.150. (a)Both plots show a positive association, but the log-salary plot is linear rather thancurved.(b)While the residuals in Figure 2.31 were positive at the beginning and end, andnegative in the middle, the log-salary residuals in Figure 2.33 show no particular pattern.
120Chapter 2Looking at Data—Relationships2.151. (a)The regression equation for predicting salary from year isˆy=41.253+3.9331x;forx=25, the predicted salary isˆy.=139.58 thousand dollars, or about $139,600.(b)The log-salary regression equation isˆy=3.8675+0.04832x. Withx=25, we haveˆy.=5.0754, so the predicted salary iseˆy.=160.036, or about $160,040.(c)Although both

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture