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. Presented is the data for beak heat loss, as a percent of total body heat loss from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.] Temperature (°C) 1515 1616 1717 1818 1919 2020 2121 2222 2323 2424 2525 2626 2727 2828 2929 3030 Percent heat loss from beak 3232 3636 3636 3333 3535 4747 5757 5151 4242 5353 4646 5252 5959 5959 6363 6262 (a) What is the equation of the least‑squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature? (Use decimal notation. Enter the values of the intercept and slope rounded to two decimal places. Enter "xx" to represent the value of the temperature.) ^y=y^= What does the slope of the least‑squares line say about the relationship between beak heat loss and temperature? Select the correct explanation. For every degree Celsius, the toucan will lose about 18%18% more heat through its beak. None of the options are correct. For every degree Celsius, the toucan will lose about 1.99%1.99% more heat through its beak. For every degree Celsius, the toucan will lose about 2.03%2.03% more heat through its beak. (b) Use the equation of the least‑squares regression line to predict beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 25 °C.25 °C. (Enter your answer rounded to two decimal places.) beak heat as a percent of total body heat loss=beak heat as a percent of total body heat loss= % (c) What percent of the variation in beak heat loss is explained by the straight‑line relationship with temperature? (Enter your answer rounded to two decimal places.) percent of variation in beak heat loss explained by the equation=percent of variation in beak heat loss explained by the equation= % (d) Find the correlation rr between beak heat loss and temperature. (Enter your answer rounded to three decimal places.) r=r= Question Source: Moore, The Basic Practice Of Statistics, 8e|Publisher: W.H. Freeman

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. Presented is the data for beak heat loss, as a percent of total body heat loss from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.] Temperature (°C) 1515 1616 1717 1818 1919 2020 2121 2222 2323 2424 2525 2626 2727 2828 2929 3030 Percent heat loss from beak 3232 3636 3636 3333 3535 4747 5757 5151 4242 5353 4646 5252 5959 5959 6363 6262 (a) What is the equation of the least‑squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature? (Use decimal notation. Enter the values of the intercept and slope rounded to two decimal places. Enter "xx" to represent the value of the temperature.) ^y=y^= What does the slope of the least‑squares line say about the relationship between beak heat loss and temperature? Select the correct explanation. For every degree Celsius, the toucan will lose about 18%18% more heat through its beak. None of the options are correct. For every degree Celsius, the toucan will lose about 1.99%1.99% more heat through its beak. For every degree Celsius, the toucan will lose about 2.03%2.03% more heat through its beak. (b) Use the equation of the least‑squares regression line to predict beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 25 °C.25 °C. (Enter your answer rounded to two decimal places.) beak heat as a percent of total body heat loss=beak heat as a percent of total body heat loss= % (c) What percent of the variation in beak heat loss is explained by the straight‑line relationship with temperature? (Enter your answer rounded to two decimal places.) percent of variation in beak heat loss explained by the equation=percent of variation in beak heat loss explained by the equation= % (d) Find the correlation rr between beak heat loss and temperature. (Enter your answer rounded to three decimal places.) r=r= Question Source: Moore, The Basic Practice Of Statistics, 8e|Publisher: W.H. Freeman

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Temperature (°C)	1515	1616	1717	1818	1919	2020	2121	2222	2323	2424	2525	2626	2727	2828	2929	3030
Percent heat loss from beak	3232	3636	3636	3333	3535	4747	5757	5151	4242	5353	4646	5252	5959	5959	6363	6262

(a) What is the equation of the least‑squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature? (Use decimal notation. Enter the values of the intercept and slope rounded to two decimal places. Enter "xx" to represent the value of the temperature.)

^y=y^=

What does the slope of the least‑squares line say about the relationship between beak heat loss and temperature? Select the correct explanation.

For every degree Celsius, the toucan will lose about 18%18% more heat through its beak.

None of the options are correct.

For every degree Celsius, the toucan will lose about 1.99%1.99% more heat through its beak.

For every degree Celsius, the toucan will lose about 2.03%2.03% more heat through its beak.

(b) Use the equation of the least‑squares regression line to predict beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 25 °C.25 °C. (Enter your answer rounded to two decimal places.)

beak heat as a percent of total body heat loss=beak heat as a percent of total body heat loss=

(c) What percent of the variation in beak heat loss is explained by the straight‑line relationship with temperature? (Enter your answer rounded to two decimal places.)

percent of variation in beak heat loss explained by the equation=percent of variation in beak heat loss explained by the equation=

(d) Find the correlation rr between beak heat loss and temperature. (Enter your answer rounded to three decimal places.)

r=r=

Question Source: Moore, The Basic Practice Of Statistics, 8e|Publisher: W.H. Freeman

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