(b) Find the equation of the least-squares line describing the relationship between y net directionality and x mean water temperature. (Round your numerical values to four decimal places.) (c) What value of net directionality would you predict for a stream that had mean water temperature of 9°C? (Round your answer to four decimal places.)

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
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Author:HOUGHTON MIFFLIN HARCOURT
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Chapter4: Writing Linear Equations
Section: Chapter Questions
Problem 14CR
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The authors of a paper investigated whether water temperature was related to how far a salamander would swim and whether it would swim upstream or downstream. Data for 14 streams with different mean water temperatures where salamander larvae were released are given (approximated from a graph that appeared in the paper).
The two variables of interest are x = mean water temperature (°C) and y = net directionality, which was defined as the difference in the relative frequency of the released salamander larvae moving upstream and the relative frequency of released salamander larvae moving downstream. A positive value of net directionality means a higher proportion were moving upstream than
downstream. A negative value of net directionality means a higher proportion were moving downstream than upstream.
y
0.3
0.2
Mean Temperature (x)
0.1
0.0
-0.1
6.22
8.01
5
8.67
10.61
12.5
11.94
12.55
18.03
18.24
(a) Construct a scatterplot of the data.
19.94
20.3
19.02
17.78
19.67
USE SALT
Net Directionality (y)
10
-0.08
15
0.25
-0.14
0.00
0.08
0.03
y
0.3
0.2
0.1
BREE
0.0
-0.1
X
20
-0.07
0.29
0.23
0.24
0.19
0.14
0.05
0.07
20
y
0.3
0.2
0.1
0.0
-0.1
5
10
15
5
10
15
20
How would you describe the relationship between x and y?
O There is an outlier in the lower right of the window. If we disregard that outlier, then there is a positive linear relationship between mean temperature and net directionality.
O There is an outlier in the lower left of the window. If we disregard that outlier, then there is a negative linear relationship between mean temperature and net directionality.
O There is an outlier in the upper right of the window. If we disregard that outlier, then there is a negative linear relationship between mean temperature and net directionality.
● There is an outlier in the upper left of the window. If we disregard that outlier, then there is a positive linear relationship between mean temperature and net directionality.
(c) What value of net directionality would you predict for a stream that had mean water temperature of 9°C? (Round your answer to four decimal places.)
y
0.3
0.2.
0.1
0.0
-0.1
(b) Find the equation of the least-squares line describing the relationship between y = net directionality and x = mean water temperature. (Round your numerical values to four decimal places.)
ŷ =
5
10
15
20
X
Transcribed Image Text:The authors of a paper investigated whether water temperature was related to how far a salamander would swim and whether it would swim upstream or downstream. Data for 14 streams with different mean water temperatures where salamander larvae were released are given (approximated from a graph that appeared in the paper). The two variables of interest are x = mean water temperature (°C) and y = net directionality, which was defined as the difference in the relative frequency of the released salamander larvae moving upstream and the relative frequency of released salamander larvae moving downstream. A positive value of net directionality means a higher proportion were moving upstream than downstream. A negative value of net directionality means a higher proportion were moving downstream than upstream. y 0.3 0.2 Mean Temperature (x) 0.1 0.0 -0.1 6.22 8.01 5 8.67 10.61 12.5 11.94 12.55 18.03 18.24 (a) Construct a scatterplot of the data. 19.94 20.3 19.02 17.78 19.67 USE SALT Net Directionality (y) 10 -0.08 15 0.25 -0.14 0.00 0.08 0.03 y 0.3 0.2 0.1 BREE 0.0 -0.1 X 20 -0.07 0.29 0.23 0.24 0.19 0.14 0.05 0.07 20 y 0.3 0.2 0.1 0.0 -0.1 5 10 15 5 10 15 20 How would you describe the relationship between x and y? O There is an outlier in the lower right of the window. If we disregard that outlier, then there is a positive linear relationship between mean temperature and net directionality. O There is an outlier in the lower left of the window. If we disregard that outlier, then there is a negative linear relationship between mean temperature and net directionality. O There is an outlier in the upper right of the window. If we disregard that outlier, then there is a negative linear relationship between mean temperature and net directionality. ● There is an outlier in the upper left of the window. If we disregard that outlier, then there is a positive linear relationship between mean temperature and net directionality. (c) What value of net directionality would you predict for a stream that had mean water temperature of 9°C? (Round your answer to four decimal places.) y 0.3 0.2. 0.1 0.0 -0.1 (b) Find the equation of the least-squares line describing the relationship between y = net directionality and x = mean water temperature. (Round your numerical values to four decimal places.) ŷ = 5 10 15 20 X
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