The toco toucan,Ramphastos toco, is the largest member of the toucan family and possesses the largest beak relative to body size of all birds. This exaggerated feature has been interpreted in various ways, 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 temperatureincreases.

The table provided contains data for beak heat loss, as a percent of total body heat loss, at various temperatures in degreesCelsius:

Temperature (C)15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 - Percent heat loss from beak 32 34 35 33 37 46 55 51 43 52 45 53 58 60 62 62

The data show that beak heat loss is higher at higher temperatures and that the relationship is roughly linear.

Regression Analysis: Percent heat loss versus Temperature - The regression equation is: Percent heat loss = 0.92 + 2.06 Temperature

Predictor Coed SE Coef T P

Constant 0.919. 5.613 0.16. 0.872

Temperature 2.0647 0.2444. 8.45. 0.000

S=4.50655 R-Sq=83.6%. R-S(adj)=82.4%

(a) What is the equation of the leastsquares regression line for predicting beak heat loss, as a percent of total body heat loss, from temperature? Let=+be the equation of the regression line. (Enter your answers rounded to two decimalplaces.)

=

=

Use the equation to predict beak heat loss, as a percent of total body heat loss from all sources, at a temperature of25

degreesCelsius. (Enter your answer rounded to two decimal places.)(b) What percent of the variation in beak heat loss is explained by the straightline relationship with temperature? (Enter your answer rounded to one decimal place.)

(25)=________

percent of the variation explained=________ %

Using the information from the figure that shows Minitab regression output, what is the correlation

between beak heat loss and temperature? (Enter your answer rounded to three decimal places.)

r=_________

How do you know whether the sign of is+ or?

Because the slope of the leastsquares regression line is positive, must be positive.

Because the intercept of the leastsquares regression line is positive,must be positive.

Because the slope of the leastsquares regression line is negative, must be positive.

Because the intercept of the leastsquares regression line is negative,must be negative.

Because the slope of the leastsquares regression line is positive, must be negative.