Answer:
Step-by-step explanation:
Hello!
The population of the study is the Toco Toucan, the largest member of the toucan family. It is believed that the length and size of the beak are due to its function of dissipating heat (a cooling mechanism).
You have two variables of interest.
X: Outdoor temperature.
Temperature (ºC) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Y: Total beak heat loss, as a percent of the total body heat loss of a toucan.
Percent heat loss from beak 33 34 33 36 36 47 52 51 41 50 49 50 55 60 60 62
The objective is to construct a least-squares regression line to predict the body heat loss of the toucans given the outdoor temperature.
Using a statistical software I estimated the regression model:
^Yi= 2.71 + 1.96Xi
1. To predict what will be the value of the beak heat loss as a percent of the total body heat loss at a temperature of 25ºC you have to simply replace the value of X in the equation:
^Yi= 2.71 + 1.96 (25)= 51.71ºC
The expected beak heat loss given an outdoor temperature of 25ºC is 51.71ºC.
2. To know what percent of the variation of the beak heat loss is explained by the outdoor temperature you have to calculate the coefficient of determination.
R²= 0.85
This means that 85% of the variability of the beak heat loss as a percent of the total body heat loss of the Toco Toucans is explained by the outdoor Temperature under the estimated model ^Yi= 2.71 + 1.96Xi
3. The correlation coefficient between these two variables is r= 0.92, this means that there is a strong positive linear correlation between the beak heat loss and the outdoor temperature. This means that when the outdoor temperature rises, the beak heat loss increases.
I hope it helps!
