Researchers have observed that bears hunting salmon in a creek often carry the salmon away from the creek before eating it. The relationship between x = total number of salmon in a creek and y = percentage of salmon killed by bears that were transported away from the stream prior to being eaten by the bear was examined in the paper “Transportation of Pacific Salmon Carcasses from Streams to Riparian Forests by Bears”(Canadian Journal of Zoology

[2009]: 195– 203). Data for the 10 years from 1999 to 2008 are given in the accompanying table.

Total Number                    Percentage Transported

19,504……………………………….                 77.8

3,460……………………………….                    28.7

1,976……………………………….                    28.9

8,439……………………………….                    27.9

11,142……………………………….                  55.3

3,467……………………………….                    20.4

3,928……………………………….                    46.8

20,440……………………………….                  76.3

7,850……………………………….                    40.3

4,134……………………………….                    24.1

a. Construct a scatterplot of these data. Does there appear to be a relationship between the total number of salmon and the percentage of transported salmon?

b. Find the equation of the least squares regression line.

c. The residuals from the least squares line are shown in the accompanying table. The observation (3,928, 46.8) has a large residual. Is this data point also an influential observation?

d. The two points with unusually large x values (19,504 and 20,440) were not thought to be influential observations even though they are far removed from the rest of the points. Explain why these two points are not influential.

e. Partial Minitab output resulting from fitting the least squares regression line is shown here. What is the value of s_e ? Write a sentence interpreting this value.

Regression Analysis: Percent Transported versus Total Number

The regression equation is

Percent Transported = 18.5 1 0.00287 Total Number

Predictor Coef

Constant 18.483

Total Number 0.0028655

S = 9.16217 R Sq = 83.2% R Sq(adj) = 81.1%

f. What is the value of r²? Write a sentence interpreting this value.

Transcribed Image Text:

Total Number Percentage Transported 77.8 28.7 28.9 279 19,504 3,460 1,976 8,439 11,142 3467 3.928 20,440 7,850 4.134 Residual 3.43 0.30 4.76 14.76 4.89 -8.02 17.06 -0.75 0.68 6.23 204 46.8 76.3 40.3 24.1