Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possible to use the cricket as a thermometer? Crickets tend to chirp more frequently as temperatures increase. This phenomenon was studied in detail by George W. Pierce, a physics professor at Harvard. In the following data, x is a random variable representing chirps per second and y is a random variable representing temperature (°F). I need help with (b) (c) (d) (e) and (f)
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possible to use the cricket as a thermometer? Crickets tend to chirp more frequently as temperatures increase. This phenomenon was studied in detail by George W. Pierce, a physics professor at Harvard. In the following data, x is a random variable representing chirps per second and y is a random variable representing temperature (°F).
I need help with (b) (c) (d) (e) and (f)
![(b) Verify the given sums Ex, Ey, Ex2, Ey2, Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.)
Ex =
Ey =
Ex2 -
Ey2 -
Exy =
(c) Find x, and y. Then find the equation of the least-squares line ý = a + bx. (Round your answer to four decimal places.)
x =
y =
(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.
y
y
120
120
100
100
80
80
60
60
40
40
20
20
5
10
15
20
5
10
15
20
120
120
100
100
80
80
60
60
40
40
20
20
5
10
15
20
5
10
15
20
(e) Find the value of the coefficient of determination 2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to four decimal places. Round your answers for the percentages to two decimal
place.)
2 =
explained
%
unexplained
(f) What is the predicted temperature hen x = 17.8 chirps per second? (Round your answer to two decimal places.)
oF](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe870b0a-6aab-4232-9112-2ec6f8d90f0c%2F27e53762-1fe6-4992-8672-d33b20395c12%2Fd1sdre_processed.png&w=3840&q=75)
![Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possible to use the cricket as a thermometer? Crickets tend to chirp more frequently as temperatures increase. This phenomenon was studied in detail by George
W. Pierce, a physics professor at Harvard. In the following data, x is a random variable representing chirps per second and y is a random variable representing temperature (°F).
19.2
15.0
20.4
17.8
16.5
15.5
14.7
17.1
y
87.8
73.4
93.1
84.7
82.2
75.2
69.7
82.0
15.4
16.2
15.0
17.2
16.0
17.0
14.4
y
69.4
83.3
79.6
82.6
80.6
83.5
76.3
n USE SALT
Complete parts (a) through (e), given Ex = 247.4, Ey = 1203.4, Ex² = 4120.44, Ey² = 97,136.54, Exy = 19,983.11, and rx 0.8778.
(a) Draw a scatter diagram displaying the data.
Graph Layers
100
Clear All
After you add an object to the graph you
96
Delete
can use Graph Layers to view and edit its
properties.
90
Fill
85
80
No
Solution
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O Help
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WebAssign. Graphing Tool](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe870b0a-6aab-4232-9112-2ec6f8d90f0c%2F27e53762-1fe6-4992-8672-d33b20395c12%2Fedf3mbt_processed.png&w=3840&q=75)
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