Climate change. Drilling down beneath a lake in Alaska yields chemical evidence of past changes in climate. Biological silicon (in milligrams of silicon per gram of water), left by the skeletons of single-celled creatures called diatoms, measures the abundance of life in the lake. A rather complex variable based on the ratio of certain isotopes relative to ocean water gives an indirect measure of moisture, mostly from snow. As we drill down, we look farther into the past. Here are data from 2300 to 12,000 years ago:
(a) Make a scatterplot of silicon (response) against isotope (explanatory). Ignoring the outlier, describe the form, direction, and strength of the relationship. The researchers say that this relationship and relationships among other variables they measured are evidence for cyclic changes in climate that are linked to changes in the sun's activity.
(b) The researchers single out one point in their plot, which they say "is an outlier that was excluded in the correlation analysis." Circle this outlier on your graph. What is the correlation with and without this point? The point strongly influences the correlation.
(c) Is the outlier also strongly influential for the regression line? Calculate and draw on your graph the regression lines with and without the outlier, and discuss what you see.