Introduction to Statistics: Chapter 4
Homework (Regression Analysis:
Exploring Associations Between
Variables)
4.1
The accompanying scatterplots show SAT scores and GPA in college for a sample of
students. The top graph uses the SAT critical reading score to predict GPA in college
and the bottom graph shows the SAT math score to predict GPA. Which is the better
predictor of GPA for thesestudents, critical reading SAT or mathSAT? Explain your
answer. - ANS The critical reading SAT is a better predictor ofGPA, because the
vertical spread of GPA is narrower.
NOTE: View the scatterplots.
In the accompanyingscatterplots, the first graph shows the years a person was
employed before working at the company and the salary at the company. The second
graph shows the years employed at the company and the salary. Which graph shows a
stronger relationship and could do a better job predicting salary at thecompany? - ANS
The years employed at the company shows a stronger relationship and is a better
predictor of salary, because the vertical spread of salary is narrower.
NOTE: View the scatterplots.
The accompanying scatterplot shows data onage, denotedA, of a sample of students
and the number of collegecredits, C, attained. Comment on thestrength, direction, and
shape of the trend. - ANS The trend islinear, positive, and strong until around age24,
when the trend becomes negative and weak.
NOTE: View the scatterplot of age and credits.
The accompanying scatterplot shows data on age and GPA for a sample of college
students. Comment on the trend of the scatterplot. Is the trendpositive, negative, or
, nearzero? - ANS The graph shows a trend near zero since the points show no pattern
as age increases. The association between age and GPA is near zero.
NOTE: View the scatterplot of age and GPA.
4.2
Complete parts(a) and(b) below. - ANS a. The scatterplot to the right shows the
college tuition and percentage acceptance at some colleges. Would it make sense to
find the correlation using this dataset? Why or whynot?
Ans: No. Linear regression is not appropriate because the trend is not linear.
b. The scatterplot to the right shows the composite grade on the ACT(American
CollegeTesting) exam and the English grade on the same exam. Would it make sense
to find the correlation using this dataset? Why or whynot?
Ans: Yes. There is no reason why linear regression would not be appropriate because
the trend is linear.
NOTE: Look at the scatterplots!
The figure shows a scatterplot of birthrate(live births per 1000women) and age of the
mother in the United States. Would it make sense to find the correlation for this data
set? Explain. According to thisgraph, at approximately what age does the highest
fertility rateoccur?
( Source: Helmut T. Wendel and Christopher S. Wendel(Editors): Vital Statistics of the
UnitedStates: Births, LifeExpectancy, Deaths, and Selected Health Data. Second
Edition, 2006, BernanPress.) - ANS Ans: No, it would not make sense to find the
correlation because the trend is not linear.
Use a computer or statistical calculator to calculate the correlation coefficient in parts a
through c below. - ANS a. The table shows the approximate distance between selected
cities and the approximate cost of flights between those cities. Calculate the correlation
coefficient between cost and miles.
Ans: r=.986
b. This table shows the sameinformation, except that the distance was converted to
kilometers by multiplying the numbers of miles by 1.609 and rounding to the nearest
kilometer. What happens to the correlation coefficient when numbers are multiplied by a
positiveconstant?
Homework (Regression Analysis:
Exploring Associations Between
Variables)
4.1
The accompanying scatterplots show SAT scores and GPA in college for a sample of
students. The top graph uses the SAT critical reading score to predict GPA in college
and the bottom graph shows the SAT math score to predict GPA. Which is the better
predictor of GPA for thesestudents, critical reading SAT or mathSAT? Explain your
answer. - ANS The critical reading SAT is a better predictor ofGPA, because the
vertical spread of GPA is narrower.
NOTE: View the scatterplots.
In the accompanyingscatterplots, the first graph shows the years a person was
employed before working at the company and the salary at the company. The second
graph shows the years employed at the company and the salary. Which graph shows a
stronger relationship and could do a better job predicting salary at thecompany? - ANS
The years employed at the company shows a stronger relationship and is a better
predictor of salary, because the vertical spread of salary is narrower.
NOTE: View the scatterplots.
The accompanying scatterplot shows data onage, denotedA, of a sample of students
and the number of collegecredits, C, attained. Comment on thestrength, direction, and
shape of the trend. - ANS The trend islinear, positive, and strong until around age24,
when the trend becomes negative and weak.
NOTE: View the scatterplot of age and credits.
The accompanying scatterplot shows data on age and GPA for a sample of college
students. Comment on the trend of the scatterplot. Is the trendpositive, negative, or
, nearzero? - ANS The graph shows a trend near zero since the points show no pattern
as age increases. The association between age and GPA is near zero.
NOTE: View the scatterplot of age and GPA.
4.2
Complete parts(a) and(b) below. - ANS a. The scatterplot to the right shows the
college tuition and percentage acceptance at some colleges. Would it make sense to
find the correlation using this dataset? Why or whynot?
Ans: No. Linear regression is not appropriate because the trend is not linear.
b. The scatterplot to the right shows the composite grade on the ACT(American
CollegeTesting) exam and the English grade on the same exam. Would it make sense
to find the correlation using this dataset? Why or whynot?
Ans: Yes. There is no reason why linear regression would not be appropriate because
the trend is linear.
NOTE: Look at the scatterplots!
The figure shows a scatterplot of birthrate(live births per 1000women) and age of the
mother in the United States. Would it make sense to find the correlation for this data
set? Explain. According to thisgraph, at approximately what age does the highest
fertility rateoccur?
( Source: Helmut T. Wendel and Christopher S. Wendel(Editors): Vital Statistics of the
UnitedStates: Births, LifeExpectancy, Deaths, and Selected Health Data. Second
Edition, 2006, BernanPress.) - ANS Ans: No, it would not make sense to find the
correlation because the trend is not linear.
Use a computer or statistical calculator to calculate the correlation coefficient in parts a
through c below. - ANS a. The table shows the approximate distance between selected
cities and the approximate cost of flights between those cities. Calculate the correlation
coefficient between cost and miles.
Ans: r=.986
b. This table shows the sameinformation, except that the distance was converted to
kilometers by multiplying the numbers of miles by 1.609 and rounding to the nearest
kilometer. What happens to the correlation coefficient when numbers are multiplied by a
positiveconstant?
