The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. The table contains data for beak heat loss, as a percentage of total body heat loss from all sources, at various temperatures in degrees Celsius. The data show that beak heat loss is higher at higher temperatures and that the relationship is roughly linear. [Note: The numerical values in this problem have been modified for testing purposes.] Temperature (Co) Percent heat loss from beak 15 32 16 34 17 35 18 33 19 37 20 46 21 55 22 51 23 43 24 52 25 45 26 53 27 58 28 60 29 62 30 62 Adapted from a graph in Glenn J. Tattersall et al., "Heat exchange from the toucan bill reveals a controllable vascular thermal radiator," Science, 325 (2009), pp. 468–470. What is the equation of the least-squares regression line for predicting beak heat loss, as a percentage of total body heat loss from all sources, from temperature? Use decimal notation. Give the values of the intercept and slope to three decimal places. Use the letter ?x to represent the value of the temperature. ?̂ = Use the equation of the least‑squares regression line to predict beak heat loss, as a percentage of total body heat loss from all sources, at a temperature of 25∘C.25∘C. Give your answer to one decimal place. ?̂ = What percentage of the variation in beak heat loss is explained by the straight‑line relationship with temperature? Give your answer to two decimal places. explained variation: Find the correlation ? between beak heat loss and temperature. Give your answer to three decimal places. ?= How do you know whether the sign of ?r is positive or negative? Correlation is positive here because the least‑squares regression line has a positive slope. Correlation is negative here because the least‑squares regression line has a negative slope. Correlation is negative here because the least‑squares regression line has a positive slope. Correlation is positive here because the least‑squares regression line has a negative slope.
The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. The table contains data for beak heat loss, as a percentage of total body heat loss from all sources, at various temperatures in degrees Celsius. The data show that beak heat loss is higher at higher temperatures and that the relationship is roughly linear. [Note: The numerical values in this problem have been modified for testing purposes.]
| Temperature (Co) | Percent heat loss from beak |
|---|---|
| 15 | 32 |
| 16 | 34 |
| 17 | 35 |
| 18 | 33 |
| 19 | 37 |
| 20 | 46 |
| 21 | 55 |
| 22 | 51 |
| 23 | 43 |
| 24 | 52 |
| 25 | 45 |
| 26 | 53 |
| 27 | 58 |
| 28 | 60 |
| 29 | 62 |
| 30 | 62 |
What is the equation of the least-squares regression line for predicting beak heat loss, as a percentage of total body heat loss from all sources, from temperature? Use decimal notation. Give the values of the intercept and slope to three decimal places. Use the letter ?x to represent the value of the temperature.
Use the equation of the least‑squares regression line to predict beak heat loss, as a percentage of total body heat loss from all sources, at a temperature of 25∘C.25∘C. Give your answer to one decimal place.
What percentage of the variation in beak heat loss is explained by the straight‑line relationship with temperature? Give your answer to two decimal places.
Find the
How do you know whether the sign of ?r is positive or negative?
Correlation is negative here because the least‑squares regression line has a negative slope.
Correlation is negative here because the least‑squares regression line has a positive slope.
Correlation is positive here because the least‑squares regression line has a negative slope.
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