Question

Researchers initiated a? long-term study of the population of American black bears. One aspect of the study was to develop a model that could be used to predict a? bear's weight? (since it is not practical to weigh bears in the? field). One variable thought to be related to weight is the length of the bear. The accompanying data represent the lengths and weights of 12 American black bears. Complete parts? (a) through? (d) below.

Total Length (cm) Weight (kg)

139.0 110

135.0 60

139.0 90

120.5 60

149.0 95

141.0 105

141.0 95

150.0 85

166.0 155

151.5 140

129.5 105

150.0 110

Critical Values for Correlation Coefficient

n
3	0.997
4	0.950
5	0.878
6	0.811
7	0.754
8	0.707
9	0.666
10	0.632
11	0.602
12	0.576
13	0.553
14	0.532
15	0.514
16	0.497
17	0.482
18	0.468
19	0.456
20	0.444
21	0.433
22	0.423
23	0.413
24	0.404
25	0.396
26	0.388
27	0.381
28	0.374
29	0.367
	0.361 (a) Which variable is the explanatory variable based on the goals of the? research? Determine the linear correlation coefficient between weight and length. Does a linear relation exist between the weight of the bear and its? length? Because the correlation coefficient is?positive negative and the absolute value of the correlation? coefficient,nothing?, is?greater not greater than the critical value for this data? set,nothing?,?a positive no a negative linear relation exists between the weight of the bear and its length.

Answer 1

(a) the explanatory variable based on the goals of the? research is Total length (cm)

(b)the linear correlation coefficient between weight and length =0.7212

(c) yes, a linear relation exist between the weight of the bear and its? length.

Critical Values for Correlation Coefficient =0.632 by using given table.

(d) Because the correlation coefficient is positive and the absolute value of the correlation? coefficient,nothing?, is greater than the critical value for this data? set,a positive linear relation exists between the weight of the bear and its length.