a. Make a scatterplot of the data. Which variable is the explanatory variable?
b. Is the association between the variables positive or negative?
c. Find the least squares regression line for predicting cancer deaths from the index of exposure. For each of the exposure indexes, compute the predicted value of cancer mortality and the associated residual.
d. What percentage of the variation in cancer deaths is explained by using the index of exposure?
e. Interpret the value of the slope in the least squares line. i.e., explain what this slope says about the change in cancer death rates for different exposure indexes.
f. Plot the residuals versus the index of exposure. What does the plot indicate about the adequacy of the linear fit?
g. Make another scatterplot of the data and include the least squares line on the plot.
h. Suppose you lived in a county with radioactive contamination index of exposure equal to 5. Use the least squares line to predict the cancer mortality in your home county.
i. Compute the correlation coefficient r between index of exposure and cancer mortality.
j. Create two new variables x* = 10x and y*=y/10.
k. Make a scatterplot of the transformed indexes and mortality rates. Does this plot have the same appearance as the plot you constructed in part a?
l. Is the correlation coefficient for the transformed values the same as the correlation coefficient for the original values?
m. Does the slope of the least squares line of y* on x* have the same slope as the regression line of y on x?
8.5, 8.9, 8.11, 8.15, 8.21, 8.23, 8.25