AP Statistics
Chapter 3: Describing Relationships Review Packet
Multiple Choice Practice
1.)For children between the ages of 18 months and 29 months, there is an
approximately linear relationship between height and age. The relationship can be
represented by = 64.93 + 0.63x, where y represents height (in centimeters) and x
represents age (in months).
Joseph is 22.5 months old. What is his predicted height?
(a) 50.80
(b) 64.96
(c) 65.96
(d) 79.11
(e) 87.40
(T.Q. 3B-1)
2.) Use the scenario #1. Loretta is 20 months old and is 80 centimeters tall. What
is her residual?
(a) -2.47
(b) 2.47
(c) -12.60
(d) 12.60
(e) 77.53
(T.Q. 3B-2)
3.) Which statements below about least-squares regression are correct?
I. Switching the explanatory and response variables will not change the
least-squares regression line.
II. The slope of the line is very sensitive to outliers with large residuals.
III. A value of r2 close to 1 does not guarantee that the relationship
between the variables is linear.
(a) I and II only
(b) I ond III only
(c) II and III only
(d) I, II, and III
(e) None of the above
(T.Q. 3B-6)
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4.) You have data for many families on the parents’ income and the years of
education their eldest child completes. Your initial examination of the data
indicates that children from wealthier families tend to go to school for longer.
When you make a scatterplot,
(a) the explanatory variable is parents’ income, and you expect to see a negative
association.
(b) the explanatory variable is parents’ income, and you expect to see a positive
association.
(c) the explanatory variable is parents’ income, and you expect to see very little
association.
(d) the explanatory variable is years of education, and you expect to see a
negative association.
(e) the explanatory variable is years of education, and you expect to see a
positive association.
(T.Q. 3B-3)
5.) An agricultural economist says that the correlation between corn prices and
soybean prices is r = 0.7. This means that
(a) when corn prices are above average, soybean prices also tend to be above
average.
(b) there is almost no relation between corn prices and soybean prices.
(c) when corn prices are above average, soybean prices tend to be below average.
(d) when soybean prices go up by 1 dollar, corn prices go up by 70 cent.
(e) the economist is confused, because correlation makes no sense in this
situation.
(T.Q. 3B-5)
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6.) A study examined the relationship between the sepal length and sepal width for
two varieties of an exotic tropical plant. Varieties X and O are represented by x’s
and o’s, respectively, in the following scatterplot. Which of the following
statements is true?
(a) Considering Variety X only, there is a positive correlation between sepal
length and width.
(b) Considering Variety O only, the least-square regression line for predicting
sepal length from sepal width has a positive slope.
(c) Considering both varieties together, there is a negative correlation between
sepal length and width.
(d) Considering each variety separately, there is a negative correlation between
sepal length and width.
(e) Considering both varieties together, the least-squares regression line for
predicting sepal length from sepal width has a negative slope.
(T.Q. 3C-6)
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Free Response Practice
For questions (7-10) How are traffic delays related to the number of cars on the
road? Below is data on the total number of hours of delay per year at 10 major
highway intersections in the western United States versus traffic volume
(measured by average number of vehicles per day that pass through the
intersection).
Below is the computer output for the regression of hours of delay versus number of
vehicle per day.
(T.Q.3B-11-13)
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7.) Describe what the scatterplot reveals about the relationship between traffic
delays and number of cars on the road.
8.) Suppose another data point at (200000, 24000), that is 200,000 vehicles per
day and 24,000 hours of delay per year, were added to the plot. What effect, if
any, will this new point have on the correlation between these two variables?
Explain.
9.) What is the slope of the regression line? Interpret the slope in the context of
this problem.
10.) Explain what the quantity S =3899.57 measures in the context of this problem.
11.) The following statistics come from 78 seventh-grade students. The x variable
represents their IQ and y represents their GPA.
x  108.9
s x  13.17
y  7.447
s y  2.10
The correlation between IQ and GPA is 0.6337
(a) Find the equation of the LSRL for predicting GPA from IQ.
(b) What percent of the observed variation in these students’ GPAs can be
explained by the linear relationship between GPA and IQ?
(c) One student has an IQ of 103 but a very low GPA of 0.53. What is the
predicted GPA for the student with IQ = 103? What is the residual for this
particular student?
(c.3.p.p)
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