5.34 ● The relationship between x 5 total number of salmon in a creek and y 5 percentage of salmon killed by bears that were transported away from the stream prior to the bear eating the salmon 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 is 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 the data.

b. Does there appear to be a relationship between the total number of salmon in the stream and the percentage of salmon killed by bears that are transported away from the stream?

c. Find the equation of the least-squares regression line. Draw the regression line on the scatterplot from Part (a).

d. The residuals from the least-squares line are shown in the accompanying table. The observation (3928, 46.8) has a large residual. Is this data point also an influential observation?
Total Number Percent Transported Residual 19,504 77.8 3.43 3,460 28.7 0.30 1,976 28.9 4.76 8,439 27.9 214.76 11,142 55.3 4.89 3,467 20.4 28.02 3,928 46.8 17.06 20,440 76.3 20.75 7,850 40.3 20.68 4,134 24.1 26.23

e. 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 in the x direction from the rest of the points in the scatterplot. Explain why these two points are not influential.

f. Partial Minitab output resulting from fitting the least-squares line is shown here. What is the value of se? Write a sentence interpreting this value.
Regression Analysis: Percent Transported versus Total Number The regression equation is Percent Transported 5 18.5 1 0.00287 Total Number Predictor Coef SE Coef T P Constant 18.483 4.813 3.84 0.005 Total Number 0.0028655 0.0004557 6.29 0.000 S 5 9.16217 R-Sq 5 83.2% R-Sq(adj) 5 81.1%
g. What is the value of r 2 for this data set (see Minitab output in Part (f ))? Is the value of r 2 large or small? Write a sentence interpreting the value of r 2.