Question

The toco toucan, the lergest member of the toucan famly, possesses the largest beek relative to body size of ell birds. This exeggerated feature hes received various interpretations, such es being e refined edaptation for feeding, However, the large surface erea mey elso be an importent mechanism for raciating heat (and hence cooing the bird)aoutdoor temperature incresses. Here are data for beok heat losss a percent of total body heat loes, at various temperatures in degrecs Celsus [Data set may be found here.) Temperature (oc) Percent heat loss from beak 32 3 35 33 37 6 SS 51 Temperature (C) percent heat loss from beak 43 52 45 53 ?8 60 62 62 15 16 17 18 19 202 22 23 24 25 2 27 28 29 30 The dats show that besk heat loss is higher ot higher temperaturcs and thot the relationship & rouchly linear. The figure below shows Minitab regreseion output for these doto Whet is the equation of the least-squares regression line for predicting beek hest loss, es a percent of total body heat loss from all sources, from temperature? (Enter your slope to four decimal places end the y-intercept to three decimal places.) n in specific language what this slope says about the relationchip between boak heat loss and tempeature. For every degree Celsius, the toucen will gen about 9.19% more heat through its beak. For very degree Celsius, the toucan will lose about 2.06% more heat through, its beak. For ovory degree Celsius, the toucan will gain ?bout 2.06% more heat through its beak. For every degree Celsius, the toucan will lose obout 9.19% more heat through its beak. (b) Use the equation of the least-squares regression ine to predict beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 23 degrees Celsius, (Round your answer to ane decimal place) (c) what percent of the variation in beak heat loss is cxolained by the straight-line relationship with temperature? (Enter your ?nswer to one dcomal place.) (d) Use the information in the figure ebove to find the correlation r betveen beak heat loss and temperature. (Round your enswer to three decimal pleces.)

Answer 1

a) the linear regression equation is :

y=0.9191+2.0647x

The linear regression equation is: y = 0.9191 + 2.0647x when x = 23, then y = 48.40 y = 0.9191 + 2.0647x y = 0.9191 + 2.0647 * 23 = 48.40 83.6% of the variation in beak heat loss with the temperature X values Sigma = 360 Mean = 22.5 Sigma(x - M_x)^2 = SS_x = 340 Y values Sigma 758 Mean = 47.375 Sigma (Y - M_y)^2 = SS_y = 1733.75 X and Y combined N = 16 Sigma(x - M_x) (Y - M_y) = 702 R calculation r = Sigma((X - M_y)(Y - M_x))/squareroot ((SS_x)(SS_y)) r = 702/ squareroot ((340)(1733.75)) = 0.9143 Meta Numerics (cross-check) r = 0.9143 The value of R is 0.9143. This is a strong positive correlation, which means that high X variable scores go with high Y variable scores

b) when x=23 , then y= 48.40

y=0.9191+2.0647x

y = 0.9191+ 2.0647 * 23 = 48.40

c)

83.6% of the variation in beak heat loss with the temperature

d)

The value of R is 0.9143. This is a strong positive correlation, which means that high X variable scores go with high Y variable scores