PRACTICE PROBLEM

For a number of years plutonium for use in atomic weapons was produced at a government facility in Hanford, Washington, USA. One of the major safety problems encountered there concerned the storage of radioactive wastes. Over the years, significant quantities of radioactive wastes, including strontium 90 and cesium 137, have leaked from their open-pit storage areas into the nearby Columbia River, which flows along the Washington-Oregon border and eventually empties into the Pacific Ocean.

To measure the health consequences of this contamination, experimenters calculated an index of exposure for each of the nine Oregon counties having frontage on either the Columbia River or the Pacific Ocean. Among the factors included in the index were the county's stream distance from Hanford and the average distance of the county's population from any water frontage. As a second variable, the cancer mortality rate was determined for each of the counties for the period 1959-1964.

The table below shows the index of exposure and the cancer mortality rate (deaths per 100,000) for the nine counties affected. Higher index values represent higher levels of contamination

 County Index of exposure (x) Cancer mortality per 100,000 (y) Umatilla 2.49 147.1 Morrow 2.57 130.1 Gillam 3.41 129.9 Sherman 1.25 113.5 Wasco 1.62 137.5 Hood River 3.83 162.3 Portland 11.64 207.5 Columbia 6.41 177.9 Clatsop 8.43 210.3

a) Plot y vs x and comment on whether the relationship is approximately linear.

b) Find the equation of the least squares line.

c)What does the slope of the line tell you about the relationship between index of exposure and mortality rate?

d)What is the predicted mortality rate for a county with a value of 4 for index of exposure?

e)What is the predicted mortality rate for a county with a value of 15 for index of exposure? Are there any problems with using the regression equation to make this prediction? (Look at the Minitab output )

f) Calculate the residual for each of the data points.

i) Verify that the sum of the residuals equals zero.
ii) Calculate the sum of squares error by squaring each of the residuals and find the sum of the squares. Confirm that this sum is the same as the sum of squares error in the ANOVA table on the computer printout.

g) What proportion of the variability in y is explained by x?

h)Calculate the correlation between index of exposure and mortality rate.