Question

The American black bear is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R. Pelton initiated a long-term study of the population of bears in the Great Smoky Mountains National Park. One aspect of the study was to develop a model that could be used to predict a bear's weight from their length. Through the data he found that the mean bear length was 130 cm (standard deviation 14 cm) and the mean weight was 100 kg (standard deviation = 28 kg). The correlation between length and weight was .80.

a. Find the equation for the regression line for predicting weight from length. (2 pts)

b. Interpret slope and y-intercept. (1 pt)

C. Suppose a 160 cm bear is captured in the field, use the regression equation to predict the weight of the bear. (1 pt)

d. The researchers were able to weigh the bear and his weight turned out to be 140 kg. Interpret the residual. (1 pt)

Answer 1

Ans:

a)r=0.80

sx=14,sy=28

x-bar=130,y-bar=100

slope=0.80*28/14=1.60

y-intercept=100-1.60*130=-108

Regression equation:

Predicted weight=1.60*length-108

b)

Slope interpretation:

For each cm of increase in length,there will be on average increase of 1.6 kg in weight.

intercept:

when length is 0,weight is -108

c)

when length=160 cm

predicted weight=1.60*160-108=148

Residual=140-148=-8

Negative value of residual indicates that predicted weight is more than the observed weight.