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Precalculus
Interpret regression lines
Read the following description of a data set.
\newline
Brett is packing for vacation and is wondering how many books to bring. He wants to make sure he does not run out of reading material, so he looks at his reading journal to see how many books he read on past vacations.For each vacation, he records the vacation's length (in days),
x
x
x
, and how many books he read,
y
y
y
.The least squares regression line of this data set is:
y
=
1.553
x
−
17.099
y = 1.553x - 17.099
y
=
1.553
x
−
17.099
\newline
Complete the following sentence:
\newline
If Brett stays on vacation for one extra day, the least squares regression line predicts that he would have read
_
_
\_\_
__
additional books.
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Read the following description of a data set.
\newline
Fans of the science fiction television show Space Cruiser Zeta are hosting a convention. To figure out how much space the event will require, an employee at the convention center looked at the space requirements for previous conventions.For each convention, the employee recorded the number of attendees,
x
x
x
, and the floor space required (in square meters),
y
y
y
.The least squares regression line of this data set is:
y
=
2.163
x
−
3
,
973.266
y = 2.163x - 3,973.266
y
=
2.163
x
−
3
,
973.266
\newline
Complete the following sentence:
\newline
The least squares regression line predicts that a convention would use
_
_
\_\_
__
additional square meters of floor space for each additional attendee.
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Read the following description of a data set.
\newline
A French car company wants to cut costs by using cheaper low-carbon steel in its car frames. To determine how varying the carbon content will affect strength, company engineers manufactured several car frames.For each car frame, the engineers noted the percentage of carbon,
x
x
x
, as well as the weight it could support (in kilograms),
y
y
y
.The least squares regression line of this data set is:
y
=
370.966
x
+
282.742
y = 370.966x + 282.742
y
=
370.966
x
+
282.742
\newline
Complete the following sentence:
\newline
If a car frame has one additional percentage point of carbon, the least squares regression line predicts it can support ___ more kilograms.
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Read the following description of a data set.
\newline
To help plan book acquisitions for the next year, a public library collected data on a sample of its active members.For each member in the sample, the library recorded the number of fiction books,
x
x
x
, and the number of nonfiction books,
y
y
y
, borrowed last month.The least squares regression line of this data set is:
y
=
4.322
x
−
44.248
y = 4.322x - 44.248
y
=
4.322
x
−
44.248
\newline
Complete the following sentence:
\newline
For each additional fiction book a library member borrowed last month, the least squares regression line predicts they borrowed ____ additional nonfiction books.
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Read the following description of a data set.
\newline
The design team at an electronics company is evaluating its new prototype for a miniature recording device. As part of this evaluation, designers at the company gathered data about competing devices already on the market. Among other things, the designers recorded the thickness of each recording device (in millimeters),
x
x
x
, and its maximum recording length (in minutes),
y
y
y
. The least squares regression line of this data set is:
y
=
38.572
x
−
547.635
y = 38.572x - 547.635
y
=
38.572
x
−
547.635
\newline
Complete the following sentence:
\newline
The least squares regression line predicts that, for each additional millimeter of thickness, a device can record
_
_
\_\_
__
additional minutes.
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Read the following description of a data set. Chloe read in a science magazine that the frequency of cricket chirps varies according to outdoor temperature. She decided to test this by making several one-minute recordings of synchronized crickets near her house.She wrote down the outdoor temperature (in Celsius),
x
x
x
, at the time of recording. Afterward, she slowed down the recording to count the number of chirps,
y
y
y
, the crickets had made.The least squares regression line of this data set is:
y
=
11.151
x
−
257.472
y = 11.151x - 257.472
y
=
11.151
x
−
257.472
Complete the following sentence: If the temperature increases by one degree Celsius, the least squares regression line predicts
_
_
\_\_
__
additional cricket chirps per minute.
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Read the following description of a data set.
\newline
Mr. Duran is offering extra credit on his statistics exam. All students have to do is state how many hours they spent studying for the exam. After he finished grading, Mr. Duran looked at how self-reported studying times were related to exam scores.He recorded the number of hours each student had reported studying,
x
x
x
, and his or her exam score (out of
100
100
100
),
y
y
y
.The least squares regression line of this data set is:
y
=
12.982
x
+
47.742
y = 12.982x + 47.742
y
=
12.982
x
+
47.742
\newline
Complete the following sentence:
\newline
For each additional hour a student had reported studying, the least squares regression line predicts that he or she would score
_
\_
_
points higher on the exam.
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Read the following description of a data set.
\newline
A selection of gemstones is showcased in the window of Greg's jewelry store. Store managers wonder if showing a greater variety will encourage more people to enter the store.The managers monitor other jewelry stores in town over one week. They note the number of gemstone types showcased at each store,
x
x
x
, as well as the number of people entering each store,
y
y
y
.The least squares regression line of this data set is:
y
=
3.785
x
+
39.148
y = 3.785x + 39.148
y
=
3.785
x
+
39.148
\newline
Complete the following sentence:
\newline
If a jewelry store showcases one additional type of gemstone, the least squares regression line predicts an additional ___ people will enter.
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One marketing professional recommends that businesses budget between
12
%
12\%
12%
and
16
%
16\%
16%
of their monthly gross sales for rent. If a business earns
$
540
,
000
\$540,000
$540
,
000
in gross sales per year, how many dollars would the adviser recommend as the maximum budget for rent each month?
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The expression
0.7
(
1.25
p
)
0.7(1.25 p)
0.7
(
1.25
p
)
represents the amount Amadou paid for dinner at a restaurant after he applied a discount coupon and added tip. Which changes to the original price could have resulted in the expression?
\newline
25
%
25 \%
25%
tip and then a discount of
30
%
30 \%
30%
\newline
0.25
%
0.25 \%
0.25%
tip and then a discount of
0.7
%
0.7 \%
0.7%
\newline
A discount of
70
%
70 \%
70%
and then
125
%
125 \%
125%
tip
\newline
A discount of
30
%
30 \%
30%
and then
0.25
%
0.25 \%
0.25%
tip
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Read the following description of a data set.
\newline
Layla has noticed that her bike ride to work takes longer on some days than others. She is curious to see how the morning temperature is related to the duration of her commute.For the past several mornings, she measured the temperature (in Celsius),
x
x
x
, and the time her commute had taken (in minutes),
y
y
y
.The least squares regression line of this data set is:
y
=
−
1.685
x
+
42.681
y = -1.685x + 42.681
y
=
−
1.685
x
+
42.681
\newline
Complete the following sentence:
\newline
The least squares regression line indicates that Layla's commute would be ___ minutes shorter if the morning temperature increases one degree Celsius.
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Read the following description of a data set.
\newline
Jack is a kinesiologist and is interested in how different athletic abilities are related. He selected several subjects with similar athletic backgrounds and compared their abilities in the long jump and the high jump.He measured how far,
x
x
x
, and how high,
y
y
y
, each subject could jump (in meters).The least squares regression line of this data set is:
y
=
0.244
x
+
0.162
y = 0.244x + 0.162
y
=
0.244
x
+
0.162
\newline
Complete the following sentence:
\newline
For each additional meter in a person's long jump, the least squares regression line predicts that he or she can clear an extra ___ meters in the high jump.
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Read the following description of a data set.
\newline
Rod Diamond is a singer who appeals to an older demographic. For a comedy segment on a late night show, he asked random people on the street how old they were and how many of his songs they could name, if any.Rod noted the age of each person he spoke with,
x
x
x
, and the number of songs each could name,
y
y
y
.The least squares regression line of this data set is:
y
=
0.054
x
−
1.247
y = 0.054x - 1.247
y
=
0.054
x
−
1.247
\newline
Complete the following sentence:
\newline
The least squares regression line predicts that if a person is one year older, they will be able to name
_
_
\_\_
__
more songs.
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Read the following description of a data set.
\newline
Researchers at a cognitive psychology lab are studying how children develop their color vocabulary. In a recent study, the researchers showed children of various ages different colored objects and asked them to name the colors.They recorded each child's age (in months),
x
x
x
, and the number of colors the child could name,
y
y
y
.The least squares regression line of this data set is:
y
=
0.213
x
−
4.937
y = 0.213x - 4.937
y
=
0.213
x
−
4.937
\newline
\newline
Complete the following sentence:
\newline
If a child were one month older, the least squares regression line predicts that he or she would be able to name
_
_
\_\_
__
additional colors.
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Read the following description of a data set.
\newline
Percy is packing for vacation and is wondering how many books to bring. He wants to make sure he does not run out of reading material, so he looks at his reading journal to see how many books he read on past vacations.For each vacation, he records the vacation's length (in days),
x
x
x
, and how many books he read,
y
y
y
.The least squares regression line of this data set is:
y
=
0.756
x
+
2.093
y = 0.756x + 2.093
y
=
0.756
x
+
2.093
\newline
Complete the following sentence:
\newline
If Percy stays on vacation for one extra day, the least squares regression line predicts that he would have read ___ additional books.
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Read the following description of a data set.
\newline
Stem and Leaf Agriculture wants to add a new compound to its bags of sunflower fertilizer. The company produced several bags containing varying amounts of the compound to see how it would affect sunflower growth.Next, Stem and Leaf collected data on the amount of the compound added to each bag (in grams),
x
x
x
, and the weekly growth of the sunflowers treated with each bag (in centimeters),
y
y
y
.The least squares regression line of this data set is:
y
=
0.138
x
+
23.221
y = 0.138x + 23.221
y
=
0.138
x
+
23.221
\newline
Complete the following sentence:
\newline
If Stem and Leaf Agriculture increased the amount of the compound by one gram per bag, the least squares regression line predicts that the sunflowers would grow
_
_
\_\_
__
centimeters more per week.
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