(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.)
(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.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
Related questions
Question
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage