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 ?Click the icon to view the data table EEB Click the icon to view the critical values table (a) Which variable is the explanatory variable based on the goals of the research? OA. The number of bears O B. The weight of the bear ° C. The length of the bear (b) Draw a scatter diagram of the data. Choose the correct graph below O A. Weight (kg) G Weight (kg) Weight (kg) C Length (cm) 18

Answer 1

a) Answer: The lenght of a bear

b) Scatter Plot

180 160 140 120 100 80 60 40 150 160 170 130 140 100 110 120

Answer: Option C)

c) Correlation Coefficient

Find X.Y, X2 and Y2 as it was done in the table below 138 135 139 120.5 149 141 141 150 166 151.5 129.5 150 110 60 90 60 95 100 110 85 155 140 105 110 15180 8100 12510 7230 14155 14100 15510 12750 25730 21210 13597.5 16500 X. X 19044 18225 19321 14520.25 22201 19881 19881 22500 27556 22952.25 16770.25 22500 Y.Y 12100 3600 8100 3600 9025 10000 12100 7225 24025 19600 11025 12100 Find the sum of every column to get ΣΧ-1710.5, ΣΥ-1220, Σ Y 1220 X·Y , Σ x2 245351.75 , ΣΥ2-132500 176572.5 Use the following formula to work out the correlation coefficient. 12 176572.5-1710.5.1220 A 0.7413 12.245351,75- 1710.5 12.132500- 12202

The linear corelation between weight and length r is = 0.741

d) Because the correlation coefficient is positive and the absolute value of coorelation coefficient r is 0.741 and the critical value for this data set is 0.576, a linear relationship exist between the weight of bear and its length