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.
Mean Temperature (x)
Net Directionality (y)
6.12
−0.08
8.11
0.25
8.57
−0.14
10.51
0.00
12.5
0.08
12.04
0.03
12.45
−0.07
17.93
0.29
18.34
0.23
19.84
0.24
20.3
0.19
19.02
0.14
17.78
0.05
19.67
0.07
(a)
Construct a scatterplot of the data.
A scatterplot has 14 points.
The horizontal axis is labeled "x" and has values from 4 to 21.
The vertical axis is labeled "y" and has values from −0.2 to 0.3.
13 points are plotted fairly scattered from approximately (4.5, 0.24) in the upper left of the window down and right to approximately (18, −0.14) in the lower right of the window.
1 point is plotted at approximately (17, 0.25) in the upper right of the window.
A scatterplot has 14 points.
The horizontal axis is labeled "x" and has values from 4 to 21.
The vertical axis is labeled "y" and has values from −0.2 to 0.3.
13 points are plotted fairly scattered from approximately (7, 0.24) in the upper left of the window down and right to approximately (20.5, −0.14) in the lower right of the window.
1 point is plotted at approximately (8, −0.15) in the lower left of the window.
A scatterplot has 14 points.
The horizontal axis is labeled "x" and has values from 4 to 21.
The vertical axis is labeled "y" and has values from −0.2 to 0.3.
13 points are plotted fairly scattered from approximately (4.5, −0.14) in the lower left of the window up and right to approximately (18, 0.24) in the upper right of the window.
1 point is plotted at approximately (17, −0.15) in the lower right of the window.
A scatterplot has 14 points.
The horizontal axis is labeled "x" and has values from 4 to 21.
The vertical axis is labeled "y" and has values from −0.2 to 0.3.
13 points are plotted fairly scattered from approximately (7, −0.14) in the lower left of the window up and right to approximately (20.5, 0.24) in the upper right of the window.
1 point is plotted at approximately (8, 0.25) in the upper left of the window.
How would you describe the relationship between x and y?
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 lower right of the window. If we disregard that outlier, then there is a positive linear relationship between mean temperature and net directionality.
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.
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.
(b)
Find the equation of the least-squares line describing the relationship between y = net directionality and x = mean water temperature. (Round your values to five decimal places.)
ŷ = +
x
(c)
What value of net directionality would you predict for a stream that had mean water temperature of 14°C? (Round your answer to five decimal places.)