Q The American black bear ( Ursus americanus ) is one of eight bear species in t
ID: 3304484 • Letter: Q
Question
Q The American black bear (Ursus americanus) is one of eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the population 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 (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 following data represent the lengths and weights of 12 American black bears.
Total Length (cm)
Weight (kg)
139.0
110
138.0
60
139.0
90
120.5
60
149.0
85
141.0
100
141.0
95
150.0
85
166.0
155
151.5
140
129.5
105
150.0
110
Which variable is the explanatory variable? Which variable is the response variable? (Hint: You need to read the problem first)
Explanatory Variable
Response Variable
Create a Scatter Diagram of the data putting the explanatory variable observations in L1 and the response variable observations in L2 on your TI-Calculator. (See Guided Notes for directions on graphing) What type of relation appears to exist between Credit Score and Interest Rate? Is it positive or negative? Is it linear? Explain using complete sentences.
Calculate the linear correlation coefficient (r). (Round 3 decimals)
Find the least squares regression line equation. (Round slope and y-intercept to 3 decimal places).
Use the least squares regression line to predict the weight of a bear who is 125 cm in length. (Round answer 1 decimals)
If length of two bears differ by 20 cm, by how much would you predict their weights to differ? (Round 1 decimals)
Calculate the coefficient of determination. (Round 3 decimals).
Total Length (cm)
Weight (kg)
139.0
110
138.0
60
139.0
90
120.5
60
149.0
85
141.0
100
141.0
95
150.0
85
166.0
155
151.5
140
129.5
105
150.0
110
Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: Weight
Independent Variable: Length
Weight = -142.47092 + 1.694168 Length
Sample size: 12
R (correlation coefficient) = 0.70390318
R-sq = 0.49547968
Estimate of error standard deviation: 20.8577
Parameter estimates:
Analysis of variance table for regression model:
Hence,
1. Explanatory variable: Total length
Response variable: Weight
2. The relationship is moderate and postive. This means that weight increases as we increase the total length.
3. r = 0.704
4. y = -142.471 + 1.694 x
5. 69.3
6. 33.9
7. 0.495
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -142.47092 77.473771 0 10 -1.8389569 0.0958 Slope 1.694168 0.54060852 0 10 3.1338167 0.0106Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.