Solution Found!
Crickets make a chirping noise by sliding their wings
Chapter 4, Problem 1CT(choose chapter or problem)
Problem 1CT
Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (in degrees Fahrenheit) and the number of chirps per second for the striped ground cricket
Temperature,x |
Chirps per Second,y |
Temperature,x |
Chirps per Second,y |
88.6 |
20.0 |
71.6 |
16.0 |
93.3 |
19.8 |
84.3 |
18.4 |
80.6 |
17.1 |
75.2 |
15.5 |
69.7 |
14.7 |
82.0 |
17.1 |
69.4 |
15.4 |
83.3 |
16.2 |
79.6 |
15.0 |
82.6 |
17.2 |
80.6 |
16.0 |
83.5 |
17.0 |
76.3 |
14.4 |
|
|
(a) What is the likely explanatory variable in these data? Why?
(b) Draw a scatter diagram of the data.
(c) Compute the linear correlation coefficient between temperature and chirps per second.
(d) Does a linear relation exist between temperature and chirps per second?
(e) Find the least-squares regression line treating temperature as the explanatory variable and chirps per second as the response variable.
(f) Interpret the slope and y-intercept, if appropriate.
(g) Predict the chirps per second if it is 83.3°F.
(h) A cricket chirps 15 times per second when the temperature is 82°F. Is this rate of chirping above or below average at this temperature?
(i) It is 55°F outside. Would you recommend using the linear model found in part (e) to predict the number of chirps per second of a cricket? Why or why not?
( j) Compute and interpret R2.
(k) A plot of residuals against temperature is shown next. Based on the residual plot, do you think a linear model is appropriate for describing the relation between temperature and chirps per second?
Questions & Answers
QUESTION:
Problem 1CT
Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (in degrees Fahrenheit) and the number of chirps per second for the striped ground cricket
Temperature,x |
Chirps per Second,y |
Temperature,x |
Chirps per Second,y |
88.6 |
20.0 |
71.6 |
16.0 |
93.3 |
19.8 |
84.3 |
18.4 |
80.6 |
17.1 |
75.2 |
15.5 |
69.7 |
14.7 |
82.0 |
17.1 |
69.4 |
15.4 |
83.3 |
16.2 |
79.6 |
15.0 |
82.6 |
17.2 |
80.6 |
16.0 |
83.5 |
17.0 |
76.3 |
14.4 |
|
|
(a) What is the likely explanatory variable in these data? Why?
(b) Draw a scatter diagram of the data.
(c) Compute the linear correlation coefficient between temperature and chirps per second.
(d) Does a linear relation exist between temperature and chirps per second?
(e) Find the least-squares regression line treating temperature as the explanatory variable and chirps per second as the response variable.
(f) Interpret the slope and y-intercept, if appropriate.
(g) Predict the chirps per second if it is 83.3°F.
(h) A cricket chirps 15 times per second when the temperature is 82°F. Is this rate of chirping above or below average at this temperature?
(i) It is 55°F outside. Would you recommend using the linear model found in part (e) to predict the number of chirps per second of a cricket? Why or why not?
( j) Compute and interpret R2.
(k) A plot of residuals against temperature is shown next. Based on the residual plot, do you think a linear model is appropriate for describing the relation between temperature and chirps per second?
ANSWER:
Answer
Step 1 of 11
(a)
The following data list the temperature (in degrees Fahrenheit) and the number of chirps per second for the striped ground cricket.
Temperature,x |
Chirps per Second,y |
Temperature,x |
Chirps per Second,y |
88.6 |
20.0 |
71.6 |
16.0 |
93.3 |
19.8 |
84.3 |
18.4 |
80.6 |
17.1 |
75.2 |
15.5 |
69.7 |
14.7 |
82.0 |
17.1 |
69.4 |
15.4 |
83.3 |
16.2 |
79.6 |
15.0 |
82.6 |
17.2 |
80.6 |
16.0 |
83.5 |
17.0 |
76.3 |
14.4 |
|
|
We are asked to find the likely explanatory variable in these data.
Temperature is the likely explanatory variable in these data since chirps per second depends on the temperature