4.30 A toucan’s beak. Exercise 3.37 (page 91) gives data on toucan beak heat loss, as a percent of total body heat loss from all sources, at various temperatures. The data show that beak heat loss is higher at higher temperatures and that the relationship is roughly linear. Figure 4.9 shows Minitab regression output for these data.

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 temperature?
Use the equation to predict beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 25 degrees Celsius.

b. What percent of the variation in beak heat loss is explained by the straight-line relationship with temperature?

c. Use the information in Figure 4.9 to find the correlation r between beak heat loss and temperature. How do you know whether the sign of r is + or − ?

Minitab X Regression Analysis: Percent heat loss versus Temperature The regression equation is Percent heat loss 0.92 +2.06 Temperature Predictor Constant Coef 0.919 SE Coef T P 5.613 0.16 Temperature 2.0647 0.2444 8.45 0.872 0.000 S = 4.50655 R-Sq = 83.6% R-Sq (adj) = 82.4%